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The 5 Best Electric Bike Batteries – 2019
For Your E-Bike Or Conversion Kit These Are The Top-Rated E-Bike Batteries
Take a look at what makes the smartest choice for purchasing the best electric bike battery and learn about the technologies, specs and standards for the top-rated e-bike batteries in How To Know Which E-Bike Battery Is Right For You later in the article.
Also see: Types of Electric Bike Conversion Kits and The Best Electric Bike Conversion Kits.
Best Electric Bike Batteries
AW 36V 10AH
Flying Horse ModWheel
Joyisi
Battery Type Lithium Lithium ion Lithium ion
Voltage 36V 36V 48V
Amperage 10 AH 11 AH 15 AH
Customer Ratings 3.5 / 5.0 Stars 4.1 / 5.0 Stars 4.4 / 5.0 Stars
Also see: Electric Bike Battery Comparison Table
Quick Answer: The 5 Best E-Bike Batteries
AW Lithium Rechargeable Battery
Mighty Max Baoshi
Universal Power Group UB12120
Best E-Bike Batteries Reviews
#1 AW Lithium Rechargeable Battery
AW 36V 10AH / 36V 14AH / 48V 14AH Lithium Rechargeable Battery at a Glance
Battery Type: Lithium
Voltage: 36V or 48V
Amperage: 10AH or 14AH
Longevity / Life: 1000 charging cycles
This AW model is a great-looking lithium battery and uses regenerative breaking to extend the battery life. It's known as a "water bottle" mount because it's lockable mount bracket bolts to a bicycle frame using the same threaded offsets as water bottle cage. The battery cell portion is lockable and removable for security.
It is absolutely necessary to waterproof this battery if it is being used in rainy conditions. Aside from that, under regular conditions, this lithium battery performs well. It has an impressive range of around 50 miles when combined with a bit of pedaling and the acceleration is also impressive.
AW offers lithium rechargeable Ebike batteries (36V 14AH and 48V 14AH) that mount on a rear rack that is included with the battery. The battery clicks into place on the rack and is locked in with a key, and is easy to remove and take indoors with you to prevent theft and in case rain is expected.
This is a popular format for Ebike batteries but sacrifices some storage space usually available on the rear rack. In general, the most powerful lithium batteries designed for electric bike conversion kits are being delivered in this format because of the ample size to accomodate the larger cell.
See the specs and current pricing for all (3) AW brand batteries at AW's Amazon seller page by clicking any of links in this review.
#2 Flying Horse ModWheel
Flying Horse ModWheel at a Glance
Over 800 charging cycles
The Flying Horse ModWheel is an expertly made piece of kit that is both reliable and powerful.
It is compatible with 250, 500, 750 and 1000 watt conversion kits, depending on the version you choose, placing it between the AW and the Joyisi in terms of power.
With 11 amp hours, It can easily exceed 20 miles in a single charge, even when used consistently.
You can attach the Flying Horse ModWheel either to a pannier rack on the back of the bike or on the down tube. Mounting is secure, sliding onto a rear rack and clicking into place. Then, you can lock it using a simple key, to stop any forward-thinking thieves from sliding it off the back.
The most expensive product on this list, the Flying Horse ModWheel has top specs, such as high-quality Panasonic cells and excellent build quality.
Although it claims only 800 charging cycles compared to the 1000 from the AW and Joyisi models, you won't be disappointed with this battery.
This e-bike battery is also available in a 48 volt 11.6 amp hour version.
#3 Joyisi
Joyisi 48V at a Glance
1000 charging cycles
The Joyisi 48 volt is a fantastic battery, jam packed with impressive power and capacity.
With 15 amp hours to draw on from one charge, the Joyisi 48 volt battery has the longest range of the items on this list, somewhere between 30 to 40 miles, depending on weight, speed, terrain etc.
The 48 volts work with 1000 watt conversion kits, meaning it is also the most powerful product we selected. This is obvious when you need it most, giving you a strong boost up hills.
It is attached to the rear of the bike via an included rack. Like the Flying Horse, you can lock your battery into place using one of the two keys provided for security and safety.
There is a useful handle attached to the back which you can flick open when sliding the battery out of the holder.
This is probably the best performance battery included here, yet cheaper than the 48 volt Flying Horse version — an awesome choice to enhance your bike.
#4 Mighty Max Baoshi
Mighty Max Baoshi at a Glance
4 X 12V
The Mighty Max Baoshi is a sealed lead acid battery which immediately puts it in a different category to the previous three.
There are four 12 volt batteries which you can add to, or take out of, a series, depending on what your conversion kit requires. This gives you the flexibility to adapt your battery to your voltage needs, but isn't as neat and discreet as the lithium batteries above.
Where these really win is in the price department. A total of 48 volts for around $165 makes them far cheaper than the 48 volts for around $460 you get from Flying Horse.
They are reliable and well built too, with shock absorbers and a spill-proof casing. The performance is not bad either, although not as good as the lithium batteries.
SLA batteries are slowly going out of fashion, but as long as the lithium batteries stay in their own league in terms of cost, batteries like the Mighty Max Baoshi will hold their place in the market for people experimenting with making electric bikes.
#5 Universal Power Group
Universal Power Group at a Glance
Universal Power Group offer two 12 volt batteries that can be run in series or alone to match your conversion kit's requirements.
At just over $50 they are a steal and good value for money for e-bike experiments. The downside to this is that they don't come with any mounting mechanism, nor a bag to attach them to the frame. The company claims them to be spill proof, so I would recommend making these (as well as all other) batteries waterproof before you head out for a spin.
In terms of performance, they simply can't be compared to the lithium batteries, the weight worsening the already poor range.
I would recommend the Universal Power Group batteries to people who are building their own e-bike and can't bear the thought of blasting up to $400 on a lithium battery.
They are not the most powerful, nor the most practical for e-bikes, but for a cheap battery that does the job, the Universal Power Group has got you covered.
Electric Bike Battery Comparison Table
Best E-Bike Batteries
AW 36V 10AH $239.95 Lithium 36V 10 AH 3.5 / 5.0 Stars
Flying Horse ModWheel $345.95 Lithium ion 36V 11 AH 4.1 / 5.0 Stars
Joyisi from $395.99 Lithium ion
48V 15 AH
4.4 / 5.0 Stars
Mighty Max Baoshi $164.99 Sealed Lead Acid
22 AH 4.0 / 5.0 Stars
Universal Power Group UB12120 $52.98 Sealed Lead Acid
How To Know Which E-bike Battery Is Right For You
Types of Batteries
Technical Factors
Maximizing Range
E-Bike Battery FAQs
In this buyer's guide Outside Pursuits leads you through everything you need to know to pick the best electric bike battery for your needs. What is the best battery for an electric bike?
Whether you're building an electric bike using a conversion kit, or you own a manufactured electric bike, we're going to help demystify the variants and evolving standards for e-bike batteries.
E-bikes as a concept stretch back well over a century, but it is only recently that they have become efficient, practical and reliable enough to hit the mass market.
Electric bicycles manage to overcome everything that is wrong with modern transport: traffic, pollution and a sedentary lifestyle, so it is no wonder the industry is on the rise.
China has led the charge and will continue to make up a huge section of the market, but with approximately 40 million units expected to be sold worldwide in 2023, the wave is expected to engulf Western Europe before heading to North America.
However, with ever-changing developments in all departments, the inner workings of electric bikes remain quite a mystery. Nowhere is this more true than in the different performance, stability and longevity of e-bike batteries.
Here at Outside Pursuits, we have made up a diverse list of the top e-bike batteries on the market at the moment, so you can explore what kind of products are out there.
Further down the page, you will find a comprehensive deconstruction of the batteries, analyzing the difference between batteries and how to get maximum performance out of them.
Choosing a different type of battery is the biggest change you will find from one product to another.
It is not just a simple question of choosing between a sealed lead-acid, nickel based battery or lithium battery, there are many variations of each type of battery and myriad results that each one has.
These batteries have been around for over 100 years, so the technology has been refined over time.
On the plus side, they are the cheapest out there and can be easily recycled. This is great for people who are building their own bikes on a limited budget.
However, with the introduction of the following two battery types, they have really been outdone in terms of performance.
They are very heavy, don't last very long, have less capacity and are more vulnerable to changing weather conditions than their rivals.
Unless price is an absolute top priority for you, or you just want to experiment building your own e-bike, my advice would be to steer clear of lead-acid batteries.
Nickel Batteries
There are no nickel-based batteries on this list due to their brief time as the cutting-edge technology, but to leave them out of a run down of e-bike batteries would be a disservice.
Nickel Cadmium
A step up in terms of energy density, nickel-cadmium can store more energy per pound than lead-acid batteries, which is one of the most important factors when choosing your e-bike battery.
Unfortunately, they are pretty poor in terms of recyclability and are quite a dangerous pollutant.
Nickel-metal Hydride
Nickel-metal hydride batteries beat cadmium versions when it comes to recyclability, and they are also more efficient, but they don't represent a massive improvement on their Cadmium cousins.
The future of nickel-based batteries looked bright for a while, but since lithium batteries came on the scene, they have been somewhat cast into the shadows.
Lithium-ion batteries have been absolute game changers in the e-bike and many other industries, and I don't think it will be long until they compete their rivals out of existence.
They improve further on the nickel batteries in terms of energy density, generating a truly impressive amount of power in exchange for very little weight. As opposed to older batteries, they also handle high and low temperatures better.
One downside is that lithium batteries are still not 100% stable (remember Samsung's PR disaster?) and far more expensive than SLA batteries, but they are rapidly improving.
Their high energy density, slow rate of discharge when not in use, low maintenance and vast range of variations have caused a great leap forward in battery technology.
Quick tip: When browsing through e-bike batteries, you will often find that they are simply referred to as "lithium batteries". Most manufacturers do not specify which variation of lithium batteries they use, but the majority, like the Flying Horse for instance, are Lithium Cobalt.
Lithium-ion Polymer Batteries
When it comes to cost, weight and range these are pretty much identical to regular lithium-ion batteries.
What sets these apart is the ability to mold them into many different shapes. What's more, they don't contain any liquid, making them resistant to overheating.
Lithium Phosphate, Lithium Cobalt and Lithium Manganese
While polymer batteries are relevant because of the way they are made, they don't refer to the chemical make up inside. Below, you can find three popular types of lithium batteries in use today.
Lithium phosphate's advantage is in extracting a larger amount of amps out of them, and therefore more power and acceleration. The downside of this is that they take up a lot of weight.
Lithium cobalt batteries are being produced in vast numbers these days, and they are used in everything from Tesla cars to laptops. They produce around double the watt hours as a lithium phosphate for the same size and weight.
Nowadays, almost all e-bike battery manufacturers that use lithium batteries go for lithium cobalt batteries over lithium phosphate, opting for a lightweight, long-range bike over a heavier, but fast-accelerating one.
Lithium manganese batteries are another result of the evolution of lithium batteries. Used in the Nissan Leaf and some elite electric bikes, it is said to be the best base for an e-bike battery currently in existence, with reportedly higher power and better range than all other lithium batteries.
Battery Technologies for the Future
One thing is for certain, advances in battery technology show no signs of stopping, so you can be sure that new variations of lithium batteries will be popping up soon enough.
Check out this list of batteries for the future and let your imagination run wild.
Batteries are nothing without a conversion kit, so before you buy, make sure you are aware of what kind of motor you have and the power it requires.
Voltage — Speed
You might remember what voltage is from high school, but here's a refresher just in case.
Voltage refers to the pressure that electricity is moved. You will notice that the SLA batteries on this list have 12 volts per pack, whereas lithium batteries can commonly handle 36 and 48 volts each.
The voltage listed for each battery refers to the standard amount that runs out of the battery, not taking into account heavy bursts, which will require a higher voltage.
A high voltage basically translates into a fast bike, and the voltage displayed represents the voltage for regular use. This fluctuates for bursts of speed.
Amp Hours (Ah) — Capacity
In simple terms, amp hours refer to charge capacity — how long your battery can supply a steady current of one single amp before it expires.
1Ah = 1 amp for 1 hour
1Ah = 2 amps for 30 minutes
1Ah = 0.5 amps for 2 hours
20Ah = 20 amps for 1 hour
20Ah = 40 amps for 30 minutes
20Ah = 10 amps for 2 hours
As a general rule, the more amp hours your bike battery has, the better. Nobody has ever complained about having too much battery supply.
Of course, having more amp hours means a more expensive battery.
Watt Hours
Watts and watt hours come into play when the electricity is converted into energy in the motor, so I'll keep this short.
Watts are determined by multiplying voltage by amperage, so 36 volts and 10 amps will create 360 watts.
Like amp hours, watt hours combines the time a motor can sustain a certain amount of watts, e.g. 360 watts for 2 hours would mean 720 watt hours.
That is useful to know, but with batteries, we're only really concerned with voltage and amp hours.
To get a good power-to-weight ratio when choosing an e-bike battery, you need a good power density. As an example, a 37 volt, 12 amp hour SLA battery from the 1990s could weigh around 36 pounds, while a 37 volt, 26 amp hour lithium battery nowadays can weigh just 10 pounds. Over twice the amp hours at less than a third of the weight.
SLA technology has improved over 20 years, but lithium batteries are still in another league when it comes to energy density. Choosing a battery with a good energy density, such as the Flying Horse, means you get a lot of power for little weight.
Replacing a battery is expensive business, so a more stable battery can save you lots of money in the long run.
SLA batteries are still much better than lithium in terms of stability and reliability, but as long as you are careful with overheating, it would be rare to have problems with lithium batteries in this day and age.
Charge Cycles
Charge cycles refer to the amount of times you can charge your battery from flat to full in one battery's lifetime.
Batteries only have a limit amount of charge cycles, around 1000 for most of these products, before they eventually stop working. This means you can get around three years of full charges every day before it dies.
The most important result you want from an electric bike battery, and an e-bike in general, is good range. Range is simply the distance you can travel on a single charge, and can be affected by the following factors:
Motor Efficiency
The topic of motor efficiency is too complicated to cover fully here, but a good motor will convert a maximum amount of electricity into forward power.
Quite a straight forward section, the more battery capacity you have, they further you can go on one charge. Just remember to charge it!
Just like a car, if you have a low tire pressure, that will be reflected in how long your battery lasts. Making your battery work to compensate for sub-optimum tire pressure is a sure-fire way of draining your battery. Keep those tires pumped up for maximum battery efficiency.
Air resistance increases at a rate of speed cubed. In practical terms, this means that as you accelerate, there is an exponential rise in resistance. Unless you're on a tight schedule, I would recommend traveling at around 15 miles per hour to get the best speed to range possible.
Hills and Acceleration
E-bikes used around San Francisco will predictably use up a lot more energy climbing up hills than an e-bike in the Netherlands. Acceleration, for all intents and purposes, puts the same strain on your battery, using up more electricity and depleting the battery faster.
Pedaling
It is logical that the less time you have your battery engaged, the more range you'll get out of it. When commuting, I try to use the battery as a "sweat saver", giving myself a boost only when the going gets tough. For flats and downhills, I prefer to give the battery a rest and do a bit of the work myself.
Similarly, I have learned that batteries really do not like standing starts. The high current needed to get your bike going is well above what is needed to maintain a moderate speed, so getting started using your feet will extend your range a bit further.
Caring for your Battery
Although batteries are manufactured, they are affected by physical conditions in the same way that living beings are. They can lose around two to three percent of their capacity per year in normal conditions even when unused, and all batteries will eventually die and be unable to recharge.
Below are a few pointers on how to extend the life of your battery.
You might have heard through the grapevine that allowing batteries to use up all of their charge prolongs their life over time.
I haven't read any reliable sources that confirm this, in fact, most recommend keeping the battery above half charge whenever possible. They work a bit like you do. If you use up all of your energy and collapse exhausted, your recovery will take a long time and it will have a negative effect on you over time.
There is plenty of comprehensive material out there that teaches you how to prolong lithium-based batteries.
When possible, batteries should be kept at around 60 degrees, as that is more or less the optimum temperature for all types of batteries.
Leaving a bike out in the cold will decrease the voltage used by your bike which can be noticed when riding, so try to store your bike, or at least the battery, indoors when possible.
Be careful to use the correct charging kit to juice up your battery. If you use an inappropriate device or continue charging once it has already reached full capacity, you can lower the amount of cycling charges.
Overcharging
Here's some good news — lithium batteries are clever. It is impossible to overcharge them, whereas nickel-based batteries can be damaged if left plugged in too long.
So don't worry about forgetting to unplug your lithium batteries, they will be fine.
Question: If my battery is at 75% and I charge it up to 100%, do I lose a charging cycle?
Not at all! You can even improve the life of a battery by not letting it die.
Try keeping your lithium batteries as close to 100% as possible.
Question: Will my battery be affected by the cold?
In the cold, lithium batteries perform much better than the SLA batteries of old, but you should try to keep your battery as close to 60 degrees as possible to avoid deterioration.
Question: How do I keep my battery from dying when not in use?
A good tip is to always keep your battery topped up when not in use. Leaving it to die is detrimental to the battery's health, so I would recommend giving it a 30 minute boost about once a week when not in use.
If you won't be using a battery for an entire season, such as winter, you should try to leave it around about 50%. All batteries discharge over time, so making sure it is at 50% for storage will prevent it from discharging completely.
Question: Can I recycle my battery?
The most common e-bike batteries, lithium-based batteries, can be recycled in the same recycling centers that you can take laptop batteries to. Most cities have a recycling center and there is even a directory of these centers. Nickel batteries, which are not commonly used any more, are a hazardous material and are very hard to recycle.
Thanks for reading How To Choose The Best Electric Bike Battery. We hope this article has helped you to discover the best choice for your needs when selecting an E-Bike battery.
Also see these informative articles, Top 10 Road Biking Routes in the United States and How To Get Started Road Biking – A Beginner's Guide.
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Lecture given to Kate O'Brien Winter School, February 2010
What I want to do in this talk is to celebrate the Irish short story and, in the process, to try to define what makes it so distinctive – and, indeed, to try and tease out what has drawn so many Irish writers to it. But in order to do so, I feel I must deal first with a strange fact, as I see it, about the Irish literature for which we're famous.
Letters to Monica. By Philip Larkin.
The decade following Philip Larkin's death in 1985 was calamitous for his reputation. On his demise, he was the most widely loved poet of his time and his passing was mourned by people for whom his beautifully crafted and deeply felt lyrics were proof that contemporary verse didn't have to be obscurantist and alienating. But in 1992 Anthony Thwaite's edition of his letters revealed a less cherishable figure, while Andrew Motion's 1993 biography mainly served to confirm that impression. (Image from www.guardian.co.uk)

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}
Following a speech by the Financial Conduct Authority in July 2017, it became apparent that Libor is expected to cease after end 2021. Regulators have actively pushed for the development of new interest rate benchmarks that are firmly anchored to actual transactions, rather than expert judgement of a handful of panel banks. These new benchmarks are generally referred to as RFRs, short for risk-free rates. We refer to them in this paper simply as overnight rates, since that is what they are based on. Libor is currently by far the most important interest rate benchmark. The transition away from Libor therefore has widespread consequences for financial products, see for example \cite{henrard2019libor} for a quantitative finance perspective. We focus in this paper in particular on the consequences for interest rate caps and floors.

A standard Libor caplet pays the difference between a Libor rate and a strike rate with a floor at zero. The payment occurs at the end of the accrual period to which the Libor rate refers, while the Libor rate itself, and therefore the caplet's payoff, is already known at the start of the accrual period. In a post-Libor world, caplets will possibly exist in two different formats. The first one, which we refer to as the \textit{backward-looking} caplet, replaces the Libor rate by the compounded overnight rate over the accrual period. This product is conceptually different from a Libor caplet, since its payoff is only known at the end of the accrual period. The second one, which we refer to as the \textit{forward-looking} caplet, replaces the Libor rate by the par rate of a single-period Overnight Index Swap (OIS) over the accrual period. This one is conceptually similar to a Libor caplet, but it requires a reliable OIS rate benchmark to be developed.\footnote{In January 2020, the ICE Benchmark Administration launched a market consultation on the introduction of an ICE swap rate based on SONIA, see \cite{ice2020sonia}. }

A natural modelling approach when working with overnight rates is to specify dynamics for the short-rate. \cite{henrard2004overnight,henrard2006skewed,henrard2019quant} and \cite{turfus2020caplet} derive explicit formulas for pricing backward-looking caplets in a single factor Gaussian short-rate model. These type of models however fail to produce a smile and can therefore only be calibrated to at-the-money caplets. This limits their practical use for traders. \cite{macrina2020rational} work with a linear-rational framework, similar to the framework in \cite{filipovic2019term}, and rely on affine transforms to obtain semi-closed form solutions for backward-looking caplet prices. In a seminal contribution, \cite{lyashenko2019looking} extend the Libor Market Model (LMM) for use with compounded overnight rates, which they refer to as the Forward Market Model (FMM). They provide explicit formulas for backward-looking caplets for the lognormal case with constant volatility, which again does not produce a smile. The FMM framework is however much more general and allows in particular for stochastic volatility dynamics as well, although calibration can prove difficult if analytic solutions for backward-looking caplet prices are not available.

In this paper we propose an extension of the SABR model introduced by \cite{hagan2002managing}. Similarly as in \cite{lyashenko2019looking}, we specify dynamics for the forward value of the compounded overnight rate over a certain accrual period. Before entering the accrual period, this rate follows standard SABR dynamics. Forward-looking caplets, whose payoff is known at the start of the accrual period, can therefore be priced using the market standard implied volatility approximation of \cite{hagan2002managing}. Once the rate enters the accrual period, it keeps evolving stochastically but its volatility is gradually scaled down to account for already realized overnight fixings. We introduce a new parameter that controls how fast the volatility is reduced and show that it can be related to the mean-reversion speed in a short-rate model. We build on the results of \cite{hagan2018managing} to derive effective constant SABR parameters that account for this time-dependent volatility scaling in the accrual period. Backward-looking caplets, which expire at the end of the accrual period, can therefore again be priced using the implied volatility approximation of \cite{hagan2002managing}, but with different parameters than forward-looking caplets. Our results allow traders to think of backward and forward-looking smiles in the same units, since we can map forward-looking SABR parameters into backward-looking ones and vice versa. \cite{piterbarg2020interest} highlights the importance of such an exercise and derives himself a correction to the initial volatility parameter in the SABR model, leaving the smile parameters unchanged. We show that this is indeed an important parameter to make an adjustment for in order to price the at-the-money backward-looking caplet correctly. For strikes away from the money, we show that an adjustment to the volatility-of-volatility parameter is important as well, in particular if we are close to or already in the accrual period.

The remaining of this paper is structured as follows. Section \ref{sec:rfr_caplets} describes the payoff of backward and forward-looking caplets. Section \ref{sec:dynamics} introduces the backward-looking SABR model. Section \ref{sec:effective} derives effective SABR parameters, which is the main contribution of this paper. Section \ref{sec:numerical} contains a numerical study of the new model. Section \ref{sec:conclusion} concludes. All proofs and auxiliary results are collected in the Appendix.

\section{Caplets in a post-Libor world}\label{sec:rfr_caplets}
Consider two times $\tau_0<\tau_1$ and define the continuously\footnote{In practice, overnight rates are compounded discretely on a daily basis, rather than continuously. For the purpose of this paper, however, this distinction is only of minor importance.} compounded overnight rate as
\begin{align*}
    R = \frac{1}{\tau_1-\tau_0}\left(e^{\int_{\tau_0}^{\tau_1} r(s)\,{\mathrm d} s}-1\right),
\end{align*}
where $r(t)$ denotes an instantaneous proxy of the overnight rate. We define for $t\le \tau_1$
\begin{align}
    R(t)= {\mathbb E}^{\tau_1}_t[R],
    \label{eq:def_Rc}
\end{align}
where ${\mathbb E}^{\tau_1}_t[\cdot]$ denotes the ${\mathcal F}_t$-conditional expectation with respect to the $\tau_1$-forward measure ${\mathbb Q}^{\tau_1}$. In other words, a swap exchanging a floating payment $R$ at $\tau_1$ against a fixed payment $K$ will have zero value at time $t$ if $K=R(t)$. Note that $R(\tau_1)=R$, since the random variable $R$ is ${\mathcal F}_{\tau_1}$-measurable.

In a post-Libor world, there will possibly be two types of caplets. The first type, which we refer to as the backward-looking caplet, pays at time $\tau_1$
\begin{align*}
    V^b_{cpl}(\tau_1) = (R(\tau_1)-K)^+,
\end{align*}
where $K$ is the strike rate. This payoff is only known at payment time $\tau_1$. The second type, which we refer to as the forward-looking caplet, pays at time $\tau_1$
\begin{align*}
    V^f_{cpl}(\tau_1) = (R(\tau_0)-K)^+.
\end{align*}
The payoff of the forward-looking caplet is already known at time $\tau_0$, but only paid at time $\tau_1$. The forward-looking caplet is therefore very similar to a traditional Libor caplet and equivalent to a single-period OIS swaption (see Remark \ref{remark:swpt}). The value at time $t\le \tau_1$ of the backward and forward-looking caplets are respectively given by:
\begin{align*}
    V_{cpl}^b(t) &= P(t,\tau_1){\mathbb E}^{\tau_1}_t[(R(\tau_1)-K)^+],\\
     V_{cpl}^f(t) &= P(t,\tau_1){\mathbb E}^{\tau_1}_t[(R(\tau_0)-K)^+],
\end{align*}
where $P(t,\tau_1)$ denotes the price at time $t$ of a zero-coupon bond with maturity $\tau_1$.

From Jensen's inequality, we get for $t\le \tau_0$
\begin{align}
    V_{cpl}^f(t)

    &\le P(t,\tau_1){\mathbb E}^{\tau_1}_t\left[{\mathbb E}_{\tau_0}^{\tau_1}\left[(R(\tau_1)-K)^+\right] \right]=  V_{cpl}^b(t).
    \label{eq:jensen}
\end{align}
Therefore, the backward-looking caplet is always worth at least as much as the forward-looking caplet, provided we have not yet entered the accrual period. The above inequality has been highlighted by several authors, e.g., \cite{lyashenko2019looking}, \cite{willems2019}, and \cite{piterbarg2020interest}. Note that we have equality in \eqref{eq:jensen} if and only if interest rates are deterministic in the accrual period.

\begin{remark}\label{remark:swpt}
By changing to the $\tau_0$-forward measure, we can express the value at time $t\le \tau_0$ of the forward-looking caplet as
\begin{align*}
    V_{cpl}^f(t) &= P(t,\tau_1){\mathbb E}^{\tau_1}_t[(R(\tau_0)-K)^+]\\
    & = P(t,\tau_0){\mathbb E}^{\tau_0}_t[P(\tau_0,\tau_1)(R(\tau_0)-K)^+].
\end{align*}
Note that $P(\tau_0,\tau_1)(R(\tau_0)-K)$ corresponds to the value at time $\tau_0$ of a spot starting single-period OIS exchanging at time $\tau_1$ a floating payment $R=R(\tau_1)$ against a fixed payment $K$. Therefore, the forward-looking caplet and the single-period OIS swaption have identical present values at time $t\le \tau_0$. Note that this is not true for the backward-looking caplet.
\end{remark}

\section{Backward-looking SABR model} \label{sec:dynamics}
From its definition in \eqref{eq:def_Rc}, we require $R(t)$ to be a ${\mathbb Q}^{\tau_1}$-martingale. Within the accrual period, i.e., for $t\in[\tau_0,\tau_1]$, $R(t)$ contains an increasing number of realized rates and this should be reflected in its volatility. With these considerations in mind, we propose the following dynamics for $R(t)$:
\begin{align}
    &{\mathrm d} R(t) = \psi(t)\sigma(t) R(t)^\beta  \,{\mathrm d} B(t), \quad\psi(t)=\min\left(1,\frac{\tau_1 - t}{\tau_1 - \tau_0}\right)^q , \label{eq:spec_R}\\
    &{\mathrm d} \sigma(t) = \nu \sigma(t)\, {\mathrm d} W(t),\quad \sigma(0)=\alpha, \label{eq:spec_sig}
\end{align}
with $q>0$, $\beta\in [0,1]$, $\alpha,\nu>0$, and $B(t),W(t)$ two ${\mathbb Q}^{\tau_1}$-Brownian motions with ${\mathrm d} B(t)\, {\mathrm d} W(t) = \rho\, {\mathrm d} t$, $\rho\in[-1,1]$.\footnote{We assume a zero lower bound for $R(t)$, however it is straightforward to accommodate an arbitrary lower bound through a displacement.} For $t\le \tau_0$, $R(t)$ follows standard SABR dynamics. For $t\ge \tau_0$, the stochastic volatility process is scaled down so that $R(t)$ becomes increasingly deterministic for $t\to\tau_1$. The newly introduced parameter $q$ controls how fast the volatility is reduced. Larger values lead to a faster reduction, see Figure \ref{fig:psi_q} for an illustration. We show in Appendix \ref{app:short-rate} that $q-1$ can be related to the mean-reversion speed of the overnight rate.

\begin{figure}
    \centering
    \includegraphics[width = 0.8\textwidth]{Figures/psi_q.eps}
    \caption{Function $\psi(t)$ for different values of $q$ with $\tau_0=0.5$ and $\tau_1 = 1$.}
    \label{fig:psi_q}
\end{figure}

Pricing forward-looking caplets, i.e., options on $R(\tau_0)$, can be done easily using the implied volatility approximations of \cite{hagan2002managing}:
\begin{align}
    &V_{cpl}^f(0) = P(0,\tau_1) \pi\left(\tau_0,K,  R(0), \sigma^f_{IV}\right),\label{eq:black_fwd}\\
    &\sigma^f_{IV} \approx \sigma_{hagan}(\tau_0,K,R(0),\alpha,\beta,\rho,\nu),\label{eq:hagan_fwd}
\end{align}
where $\pi(\cdots)$ denotes \cite{black1976pricing}'s formula  and $\sigma_{hagan}(\cdots)$ denotes the Black implied volatility approximation of \cite{hagan2002managing}, see Appendix \ref{sec:black_hagan} for explicit expressions.\footnote{Remark that \eqref{eq:black_fwd}-\eqref{eq:hagan_fwd} only makes sense for $\tau_0>0$. For $\tau_0 \le 0$, we have $V_{cpl}^f(0)=P(0,\tau_1)(R(\tau_0) -K)^+$.}  Pricing backward-looking caplets, i.e., options on $R(\tau_1)$, is more involved because of the time dependence through the function $\psi(t)$. In the next section we derive effective SABR parameters $\hat{\alpha}$, $\hat{\rho}$, $\hat{\nu}$ such that
\begin{align}
    &V_{cpl}^b(0) = P(0,\tau_1) \pi\left(\tau_1,K,  R(0), \sigma^b_{IV}\right),\label{eq:black_bwd}\\
    &\sigma^b_{IV} \approx \sigma_{hagan}(\tau_1,K,R(0),\hat{\alpha},\beta,\hat{\rho},\hat{\nu}).\label{eq:hagan_bwd}
\end{align}
We leave $\beta$ unchanged, since the local volatility component in the backward-looking SABR model has not changed compared to the standard SABR model. Note the difference between \eqref{eq:black_fwd}-\eqref{eq:hagan_fwd} and \eqref{eq:black_bwd}-\eqref{eq:hagan_bwd} in the time-to-exercise parameter, which reflects the fact that the forward-looking rate fixes at $\tau_0$ while the backward-looking rate fixes at $\tau_1$. Also note that no additional treatment is required for pricing a backward-looking caplet with $\tau_0 < 0$, i.e., when some of the rate fixings in the payoff have already realized.

We see two practical use cases for the backward-looking SABR model. Suppose first that we observe liquid prices for both backward and forward-looking caplets at a range of strikes. One possibility is to fix $q$ to an exogenous value (e.g., based on historical data), and then use the model to separately mark two sets of parameters $(\alpha, \rho, \nu)$ to backward and forward-looking caplet prices.\footnote{The parameter $\beta$ is typically not calibrated to market prices, but rather to historical data or expert judgement.} The forward-looking parameter markings are just the standard SABR parameters. The backward-looking parameter markings represent the prices of the corresponding forward-looking caplets in the standard SABR model. The purpose of the backward-looking SABR model extension is in this case to make the two sets of marked parameters comparable, since it takes care of the additional volatility in the accrual period under the hood of the model. This allows a trader to easily compare how expensive or cheap the backward-looking caplet is versus the forward-looking one. Alternatively, we can opt to use a single set of parameters for both backward and forward-looking caplets. Suppose for example that prices of forward-looking caplets are more liquid. In this case, we could mark $(\alpha,\rho,\nu)$ to forward-looking caplets, and mark $q$ to hit the at-the-money backward-looking caplet.

\begin{remark}\label{remark:change_ttm}
We choose to derive effective SABR parameters with respect to a time-to-exercise parameter $\tau_1$,  since this is the only choice that allows to price backward-looking caplets throughout the entire accrual period. We note however that it is straightforward to transform these parameters to correspond to a different time-to-exercise parameter $T>0$ using the relationship\footnote{This relationship follows from a simple time-change argument in the SABR model. One can directly verify that it also holds in the implied volatility approximation of \cite{hagan2002managing}.}
\[
\pi(\tau_1,K,R(0),\sigma_{hagan}(\tau_0,\hat{\alpha},\beta,\hat{\rho},\hat{\nu})) =
\pi\left(T,K,R(0),\sigma_{hagan}\left(T,\hat{\alpha}\sqrt{\frac{\tau_1}{T}},\beta,\hat{\rho},\hat{\nu}\sqrt{\frac{\tau_1}{T}}\right)\right).
\]
For example, when $\tau_0>0$ we can express the effective parameters in terms of a time-to-exercise parameter $\tau_0$ by simply multiplying $\hat{\alpha}$ and $\hat{\nu}$ by $\sqrt{\frac{\tau_1}{\tau_0}}$.
\end{remark}

\begin{remark}
The dynamics in \eqref{eq:spec_R}-\eqref{eq:spec_sig} are in fact a special case of the general FMM model introduced by \cite{lyashenko2019looking} for once specific tenor. Our results can therefore be used to construct a SABR style FMM model with analytic prices for both backward and forward-looking caplets.
\end{remark}

\section{Backward-looking effective SABR parameters}\label{sec:effective}
We apply the results of \cite{hagan2018managing} to find effective SABR parameters $\hat{\alpha}$, $\hat{\rho}$, $\hat{\nu}$ for the model in \eqref{eq:spec_R}-\eqref{eq:spec_sig}. Their results, based on singular perturbation techniques and effective medium theory, are not exact but have the same accuracy as the original SABR approximation of \cite{hagan2002managing}. We distinguish two cases, based on the sign of $\tau_0$.

If $\tau_0\le 0$, then part of the backward-looking caplet's payoff has realized already. In this case $\psi(t)$ is strictly decreasing towards zero as time moves forward, which decreases the volatility of $R(t)$. The following theorem presents effective SABR parameters incorporating this time-dependent volatility scaling:
\begin{theorem}\label{thm:tau0Negative}
If $\tau_0\le 0$, then the backward-looking effective SABR parameters are
\begin{align*}
&\hat{\rho} = \frac{2\rho}{\sqrt{\zeta}(3q+2)},\quad  \hat{\nu}^2 = \nu^2 \zeta (2q+1),
\quad\hat{\alpha}^2 = \frac{\alpha^2}{2q+1}\left(\frac{\tau_1}{\tau_1-\tau_0}\right)^{2q} {\rm e}^{\frac{1}{2}(\frac{\nu^2}{q+1} - \hat{\nu}^2)\tau_1},
\end{align*}
where we have defined
\[
\zeta = \frac{3}{4q+3}\left(\frac{1}{2q+1} + \rho^2\frac{2q}{(3q+2)^2}\right).
\]
\end{theorem}
\begin{proof}
See Appendix.
\end{proof}
Remark that the effective smile parameters $\hat{\rho}$ and $\hat{\nu}$ in Theorem \ref{thm:tau0Negative} do not depend on $\tau_0$ and $\tau_1$, which is linked to a particular scaling property of the backward-looking SABR model when $\tau_0\le 0$.
To see this, define the processes $R'(t)$ and $\sigma'(t)$ as
\[
R'(t) = R(\tau_1 t),\quad \sigma'(t)=\sqrt{\tau_1} \left(\frac{\tau_1}{\tau_1-\tau_0}\right)^q\sigma(\tau_1 t).
\]
Using It\^o's lemma and time-scaling properties of the Brownian motion we get for $t\ge \tau_0$
\begin{align*}
&{\mathrm d} R'(t) = R'(t)^\beta(1-t)^q\sigma'(t)\,{\mathrm d} B(t),\quad  {\mathrm d} \sigma'(t) = \nu \sqrt{\tau_1} \sigma'(t)\,{\mathrm d} W(t).
\end{align*}
Hence, if $\tau_0\le 0$, then the time-0 price of a backward-looking caplet with accrual period $[\tau_0,\tau_1]$ is equivalent to one with canonical accrual period $[0,1]$ together with the following re-parameterization
\begin{equation}
\alpha\to \alpha \sqrt{\tau_1}\left(\frac{\tau_1}{\tau_1-\tau_0}\right)^q,\quad \nu\to\nu\sqrt{\tau_1}.
\label{eq:subs}
\end{equation}
In other words, starting from effective parameters for the accrual period $[0,1]$, one can obtain the effective parameters for any accrual period $[\tau_0,\tau_1]$, $\tau_0\le 0<\tau_1$, by first making the substitutions \eqref{eq:subs} and then adjusting for the change in time-to-exercise from $1$ to $\tau_1$ (see Remark \ref{remark:change_ttm}). One can easily verify that this scaling property is indeed satisfied for the effective parameters in Theorem \ref{thm:tau0Negative}.\footnote{Note that the scaling property is not guaranteed to hold a priori, since the effective parameters in Theorem \ref{thm:tau0Negative} are only approximations. The fact that it does hold is comforting.} In particular, since there is no dependence on $\alpha$ or $\nu$ in $\hat{\rho}$, the effective correlation does not depend on the accrual period. At first sight, the effective volatility-of-volatility may have a dependence on $\tau_1$ through the substitution \eqref{eq:subs}, however this is offset by the subsequent change in time-to-exercise from $1$ to $\tau_1$.

The only effective parameter that depends on how far we are in and how much is remaining of the accrual period is therefore $\hat{\alpha}$. The exponential factor in $\hat{\alpha}$ is a second order correction and does typically not contribute much. At the start of the accrual period, i.e., when $\tau_0=0$, $\hat{\alpha}^2$ is roughly $(2q+1)$ times smaller than $\alpha^2$. The fact that $\hat{\alpha}^2$ is smaller than $\alpha$ is intuitive. Indeed, by increasing the time-to-exercise from $\tau_0$ to $\tau_1$ we increase the option value, ceteris paribus. However, because of the volatility reduction in the accrual period we have increased the option value too much and need to bring it down again with a smaller effective $\hat{\alpha}$. When we price further in the accrual period, i.e., when we decrease $\tau_0$ and $\tau_1$, then $\hat{\alpha}$ gradually decreases towards zero, which reflects the fact that an increasing part of the compounded overnight rate has realized already.

If $\tau_0\ge 0$, then none of the rates referenced in the backward-looking caplet's payoff have been realized yet as of pricing time 0. The rate $R(t)$ follows standard SABR dynamics for $t\le \tau_0$, and only afterwards will the volatility process be scaled down towards zero as $t\to \tau_1$. The following theorem provides the effective SABR parameters in this case.

\begin{theorem}\label{thm:tau0Positive}
If $\tau_0\ge 0$, then the backward-looking effective SABR parameters are
\begin{align*}
&\hat{\rho} = \rho \frac{3\tau^2 + 2q\tau_0^2 + \tau_1^2}{\sqrt{\gamma}(6q+4)},\quad
 \hat{\nu}^2 = \nu^2 \gamma \frac{2q+1}{\tau^3\tau_1},\quad
\hat{\alpha}^2 =\frac{ \alpha^2}{2q+1}\frac{\tau}{\tau_1}{\rm e}^{\frac{1}{2}H\tau_1},
\end{align*}
where we have defined
\begin{align*}
& \tau = 2q\tau_0 + \tau_1,\quad H = \nu^2\frac{\tau^2 +2q\tau_0^2 + \tau_1^2}{2\tau_1\tau(q+1)} - \hat{\nu}^2,\\
&\gamma =\tau
\frac{2\tau^3 + \tau_1^3 + (4q^2-2q)\tau_0^3 + 6q\tau_0^2\tau_1}{(4q+3)(2q+1)}+3q\rho^2 (\tau_1-\tau_0)^2\frac{
3\tau^2 - \tau_1^2 +5q\tau_0^2 + 4\tau_0\tau_1}{(4q+3)(3q+2)^2}.
\end{align*}
\end{theorem}
\begin{proof}
See Appendix.
\end{proof}

When pricing at the start of the accrual period, i.e., when $\tau_0 = 0$, the effective parameters in Theorem \ref{thm:tau0Negative} and \ref{thm:tau0Positive} agree. For $\tau_1=\tau_0>0$, the backward-looking SABR model reduces to the standard SABR model and Theorem \ref{thm:tau0Positive} indeed gives in this case $\hat{\rho}=\rho$, $\hat{\nu}=\nu$, and $\hat{\alpha}=\alpha$.

In Figure \ref{fig:effectiveParams}, we set $\tau_1-\tau_0 = 0.5$, $q=1$, $\rho = -50\%$, $\nu = 50\%$, and plot the ratios $\hat{\rho}/\rho$, $\hat{\nu}/\nu$, and $\hat{\alpha}/\alpha$ for $\tau_0\in[-0.5,5]$. We observe that the impact is strongest for small $\tau_0$ and becomes less noticeable for larger $\tau_0$. This makes sense intuitively, since for large $\tau_0$, the model behaves like the standard SABR model most of the time. We also observe that the effective correlation does not change much, while the effective volatility-of-volatility and the initial volatility are reduced substantially for small $\tau_0$.

\begin{figure}[h]
\centering
\begin{subfigure}{.45\textwidth}
  \centering
  \includegraphics[width=\textwidth]{Figures/rho_eff.eps}
  \caption{$\hat{\rho}/\rho$}
  \label{fig:rhoEff}
\end{subfigure}
\begin{subfigure}{.45\textwidth}
  \centering
  \includegraphics[width=\textwidth]{Figures/alpha_eff.eps}
  \caption{$\hat{\alpha}/\alpha$}
  \label{fig:alphaEff}
\end{subfigure}
\begin{subfigure}{.45\textwidth}
  \centering
  \includegraphics[width=\textwidth]{Figures/nu_eff.eps}
  \caption{$\hat{\nu}/\nu$}
  \label{fig:nuEff}
\end{subfigure}
\caption{Ratio of effective SABR parameters over original ones for $\tau_0\in[-0.5,5]$. Parameter choices: $\tau_1-\tau_0 = 0.5$, $q=1$, $\rho = -50\%$, $\nu = 50\%$.}
\label{fig:effectiveParams}
\end{figure}

For $q\to\infty$, the volatility of $R(t)$ is reduced to zero immediately after the start of the accrual period. In this limit case, the backward looking and forward-looking caplet should have the same price. Taking the limit $q\to\infty$ for the effective parameters in Theorem \ref{thm:tau0Positive} gives
\[
\lim_{q\to\infty}\hat{\rho} = \rho,\quad \lim_{q\to\infty}\hat{\nu}^2 = \nu^2 \frac{\tau_0}{\tau_1},\quad \lim_{q\to\infty} \hat{\alpha}^2 = \alpha^2\frac{\tau_0}{\tau_1}.
\]
Recall that the effective parameters $\hat{\alpha},\hat{\rho},\hat{\nu}$ correspond to a time-to-exercise parameter $\tau_1$, while $\alpha, \rho, \nu$ correspond to a time-to-exercise parameter $\tau_0$. From the observation in Remark \ref{remark:change_ttm} we immediately see that the backward and forward-looking caplet indeed have equal price in this limit case. Taking the limit $q\to\infty$ for the effective parameters in Theorem \ref{thm:tau0Negative} gives zero values for all effective parameters, which is not surprising since there is no volatility left in the accrual period. For $q\to 0$, the volatility decays very slow in the accrual period. Taking the limit $q\to 0$ for the effective parameters in Theorem \ref{thm:tau0Negative} and Theorem \ref{thm:tau0Positive} gives
\[
\lim_{q\to 0}\hat{\rho} = \rho,\quad \lim_{q\to 0}\hat{\nu}^2 = \nu^2,\quad \lim_{q\to 0} \hat{\alpha}^2 = \alpha^2.
\]
The effective parameters therefore coincide with the original ones. However, we note again that because of the difference in the corresponding time-to-exercise parameter, this does not mean that the backward and forward-looking caplet have the same price. In fact, in the limit case $q\to 0$, the difference between the two is maximized.

\begin{remark}
\cite{piterbarg2020interest} derives for $\tau_0>0$ an adjusted initial volatility
\begin{equation}
    \tilde{\alpha} = \alpha\sqrt{1+\frac{\tau_1 -\tau_0}{3\tau_0}}\label{eq:piterbarg_alpha}
\end{equation}
such that
\begin{align*}
    &V_{cpl}^b(0) = P(0,\tau_1)\pi(\tau_0,K,R(0),\tilde{\sigma}_{IV}^b),\\
    &\tilde{\sigma}_{IV}^b \approx \sigma_{hagan}(\tau_0, K, R(0), \tilde{\alpha}, \beta, \rho, \nu).
\end{align*}
Note that $\tilde{\alpha}$ corresponds to a time-to-exercise $\tau_0$. In order to compare $\hat{\alpha}$ with $\tilde{\alpha}$, we need to scale it appropriately (see Remark \ref{remark:change_ttm}):
\begin{align}
    \hat{\alpha}\sqrt{\frac{\tau_1}{\tau_0}} = \alpha\sqrt{\frac{\tau}{(2q+1)\tau_0}} {\rm e}^{\frac{1}{4}H\tau_1}
    = \alpha\sqrt{1+\frac{\tau_1 -\tau_0}{(2q+1)\tau_0}}{\rm e}^{\frac{1}{4}H\tau_1}.\label{eq:piterbarg_adjustment}
\end{align}
Ignoring the exponential factor, which is typically very close to one, and setting $q=1$, we observe that \eqref{eq:piterbarg_alpha} agrees with \eqref{eq:piterbarg_adjustment}.
\end{remark}

\section{Numerical study}\label{sec:numerical}
In order to evaluate the approximation quality of the effective SABR parameters derived in the previous section, we perform a Monte-Carlo simulation of the model as a benchmark. We arbitrarily choose the following parameter values: $\beta=1$, $R(0) = 0.05$, $\tau_0 = 0.5$, $\tau_1 = 1$, $\rho = -0.50$, $\nu = 0.50$, $\alpha = 0.10$, and $q=1$. The effective parameters, computed using Theorem \ref{thm:tau0Positive}, become
\[
\hat{\alpha} = 0.082,\quad \hat{\rho} = -0.503,\quad \hat{\nu} = 0.411.
\]
We simulate \eqref{eq:spec_R}-\eqref{eq:spec_sig} using a log-Euler discretization scheme with time step $1/512$ and $10^6$ simulation trajectories. Figure \ref{fig:simulated_rate} shows an example of three simulated trajectories of $R(t)$. Notice how the volatility starts to decrease for $t>\tau_0$. We use the simulated trajectories to price backward-looking caplets and then compute Black implied volatility by inverting \cite{black1976pricing}'s formula. Figure \ref{fig:MC_smile} shows that \cite{hagan2002managing}'s implied volatility approximation with effective parameters
$\hat{\alpha}, \hat{\rho}, \hat{\nu}$ produces virtually identical results as the Monte-Carlo simulation. As a reference, we also plot implied volatilities computed using  \cite{hagan2002managing}'s approximation with parameters $\alpha, \rho, \nu$ and $\hat{\alpha}, \rho, \nu$. In the first case, we do not apply any adjustments to the SABR parameters, and Figure \ref{fig:MC_smile} clearly shows we are substantially mispricing caplets at all strikes. In the second case, we only apply a correction to the initial volatility parameter. The at-the-money strike is priced correctly in this case, but strikes away from the money are not.

\begin{figure}
    \centering
    \includegraphics[width=0.8\textwidth]{Figures/simulated_rate.eps}
    \caption{Three simulated trajectories of $R(t)$. The vertical black line indicates the start of the accrual period $t=\tau_0$.}
    \label{fig:simulated_rate}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=0.8\textwidth]{Figures/MC_smile.eps}
    \caption{Black implied volatility smiles. The blue line corresponds to the Monte-Carlo price, the orange line to the SABR price with $(\hat{\alpha}, \hat{\rho}, \hat{\nu})$, the green line to SABR price with $(\hat{\alpha}, \rho, \nu)$, and the red line to the SABR price with $(\alpha, \rho, \nu)$.}
    \label{fig:MC_smile}
\end{figure}

\section{Conclusion}\label{sec:conclusion}
We have presented a natural extension of the SABR model to consistently price backward and forward-looking caplets. Forward-looking caplets can be priced using the market standard approximations of \cite{hagan2002managing}. Building on the results of \cite{hagan2018managing}, we have derived closed-form effective SABR parameters for pricing backward-looking caplets. We have shown the effective SABR approximation to be highly accurate when compared to a Monte-Carlo simulation benchmark. The correction to the initial volatility and the volatility-of-volatility parameters are most pronounced, while the correction to the correlation parameter is of second order importance. Our results allow traders to think of backward and forward-looking caplets in normalized units, which helps to assess their relative values. A similar analysis can be done for the \cite{heston1993closed} model using, for example, the results from \cite{hagan2018implied}. We leave such extensions for future research.
\clearpage

redpajama_set_name: RedPajamaArXiv


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If you decide to join our mailing list through the sweepstakes, please refer to the top of this section above that describes mailing lists.
For more information about a given sweepstakes, please review that sweepstakes' specific Terms & Conditions. Or you may request a copy from us by emailing us
Information in this section, "Sweepstakes," will be used to notify potential winners and to maintain a winners' list, the latter of which we are required to provide to the community upon request.
Non-personal interactions with LMG: In both instances below, we do not store the information collected in our servers.
When you connect to our website, our web servers recognize your IP address and certain other information about your computer. This is necessary to facilitate transactions, administer the web server, and track down problems.
LMG may also use "cookie" technology to gather information on Internet use in order to serve you more effectively. Usage of cookies may be linked to personally identifiable information. You can set your browser to remove or reject cookies; you do not need to accept cookies to use LMG.
Except as otherwise specified, all the information in this Section 3 of the Privacy Policy that is stored is maintained solely by LMG. We do not sell or rent information to third parties or share information in ways other than disclosed in this Privacy Policy.
4. What about Third Party Data Collection?
If you use certain features on the Site, it may enable third parties to collect data about your use as follows:
Credit or Debit Card Payment: LMG utilizes Stripe to process rental payments and other fees on the Site. LMG does not itself store debit or credit card information. We only collect this information, send it to Stripe, and then Stripe sends us back a multi-use token that we store in our servers. This token is unique to a specific card with a specific merchant, and ensures only LMG can ever use the token to process subsequent transactions.LMG utilizes this feature for a customer's convenience so you do not have to reenter credit card information. You should review Stripe's Privacy Policy for more detail about how your credit or debit card information will be stored and maintained.
Social Plug-Ins: Users may follow or like LMG, or recommend LMG using social plug-ins such as for Google+, Facebook, Twitter, LinkedIn, and Pinterest. Users should review the privacy policies of Google, Facebook, Twitter, LinkedIn, and Pinterest for more detail about information collected from these sites. Our plugins are powered by AddThis, their privacy policy is also available here.
Courier services: LMG may use courier services (Lyft or Uber) to handle delivery or pickup of Item(s) to you. In order to utilize these services, LMG may release your contact information (e.g., email, phone, name) and addresses. Please review the privacy policies of these couriers for more information: UberRUSH, Lyft.
MixPanel Analytics: LMG also uses MixPanel to learn how our customers use the Site and Services. MixPanel utilizes cookies and web beacons to track customer usage. For more information on MixPanel's data collection and use practices, see the MixPanel Privacy Policy. You can opt-out of MixPanel's automatic retention of data collected by clicking here: MixPanel Opt-Out. If you get a new computer, install a new browser, erase or otherwise alter your browser's cookie file (including upgrading certain browsers) you may also clear the MixPanel opt-out cookie, and have to reset it by visiting the link above.
Users are encouraged to use available controls and settings on your device to reflect your privacy preferences.
5. Is Information Ever Disclosed by LMG to Third Parties?
Information collected by LMG may be disclosed in the following circumstances.
When Disclosure is Required By Law: Information may be provided where we are required to do so by law, or if we believe in good faith that it is reasonably necessary (i) to respond to claims asserted against LMG or to comply with the legal process (for example, discovery requests, subpoenas or warrants); (ii) to enforce or administer our policies and agreements with Users; (iii) for fraud prevention, risk assessment, investigation, customer support, product development and de-bugging purposes; or (iv) to protect the rights, property or safety of LMG, its Users or members of the general public. We will use commercially reasonable efforts to notify Users about law enforcement or court ordered requests for data unless otherwise prohibited by law.
Acquisition/Merger/Assignment: Information may be disclosed if LMG is involved in any merger, acquisition or assignment of its interests. Under such circumstances, LMG will use commercially reasonable efforts to notify its Users if their personal information is to be disclosed or transferred and/or becomes subject to a different privacy policy.
Winners' List for Sweepstakes: We are required to provide to anyone who requests it a list of the winners for any of our sweepstakes. This information includes name and email, as described in Section 3.
6. What is LMG's Security Policy?
We have implemented reasonable administrative, technical and physical security measures to protect your personal information against unauthorized access, destruction or alteration of your information. However, Users should be advised that no method of transmission over the Internet and no method of storing electronic information can ever by 100% secure.
7. Response to "Do Not Track" Signals
"Do Not Track" is a feature enabled on some browsers that sends a signal to request that a web application disable its tracking or cross-site user tracking. At present, LMG does not respond to or alter its practices when a "Do Not Track" signal is received.
This Privacy Policy covers the collection, use, and disclosure of Personal Data/Personally Identifiable Information (as defined by applicable law and hereinafter collectively referred to as "Personal Data") when visitors and Customers (collectively "Users") interact in-person, by phone, or otherwise access lastmingear.com (the "Site") and/or the related mobile applications (collectively the "Platform") and the software and services made available through the Platform.
The Platform is owned and operated by Catchbright, LLC doing business as Last Minute Gear with offices in the United States. This Policy governs the data collection practices when you interact with Last Minute Gear (hereinafter referred to as "LMG"). LMG collects Personal Data from its Users around the world and processes, transfers and stores data within the United States. By checking the "I consent to the Privacy Policy" box and subject to your opt-in/opt-out preferences, you consent to the collection, use and disclosure practices identified in this Privacy Policy.
All capitalized terms and phrases used herein but not otherwise defined shall have the same meanings given to them in LMG's Terms of Service.
1. What Information is Collected by LMG And How Is It Used?
Customer Orders: When you initiate an Order, whether the Order is completed or not, LMG may request and store:
Credit or Debit Card Information: Address, and credit card numbers are collected to process payment. LMG does not store this information ourselves in our servers. We work with a third party provider, Stripe, and save only a token they provide back to us, in order to guarantee the security of your information (see Section 2).
Order-related information collected by LMG will be utilized to (i) fulfill an Order and/or (ii) assist in any dispute resolution. Emails will also be utilized to provide technical, service-related and marketing communications regarding our Services; and/or communicate material changes to our Terms of Service and Privacy Policy. Customers may unsubscribe from marketing communications at any time through the opt-out link contained within those communications or by contacting LMG at [email protected].
Subscribe to Mailing List or Request Additional Information: Users may optionally provide their email address to subscribe to our mailing list or to request additional information regarding our products and services. All Users may unsubscribe at any time through the opt-out link contained within those communications or by contacting LMG at [email protected].
Sweepstake Entries: When you participate in a LMG-sponsored sweepstakes, we will collect and store entrants' names and emails. This information will be collected even if you initiate, but do not complete, a sweepstakes entry. Entrants may also optionally elect to opt-in to join our mailing list. Information collected will be used to notify potential winners and to maintain a winner's list as required by applicable law. LMG is required to provide to any third party, upon request, the name of LMG sweepstakes winners.
Other interactions with LMG: Additionally, data may be collected and stored when you:
Voluntarily respond to surveys based on your experience with LMG. Information provided will be used to better improve our services. If we were to release any insights or analytics information from these surveys, we would report data only in its anonymous and aggregate form, without any personally identifiable information or reference to individual User.
IP Addresses, Web Beacons, & Cookies: When a User accesses the Site, our web servers recognize your IP address and certain other information about your computer. This is necessary to facilitate transactions, administer the web server, and track down problems. LMG utilizes web beacon & cookie technology to gather information on Internet use in order to serve Users more effectively. As described in Section 2, LMG also utilizes third party analytics services which may also use tracking cookies to provide information about the use of our Platform. Users can set their browser to remove or reject cookies and/or accept or refuse cookies on the cookie consent banner on the Site itself. You can also manage cookies for any online advertising service via the consumer choice tools created under self-regulation programs, such as the US-based aboutads.info/choices page or the European Union ("EU") based Your Online Choices. Please be advised, however, that some Platform features/services may not function properly without cookies.
2. Is Information Collected By Or Disclosed To Third Parties?
LMG does not sell, trade, rent, or lease Personal Data to any third parties. LMG utilizes and shares Personal Data with the following data processors:
Hosting Services: LMG stores all data generated on or through the Platform on Heroku to facilitate its cloud hosting services. Users should click on the hyperlink for more information on its data collection and privacy practices.
Credit or Debit Card Payment: LMG will collect Customer credit card information (including credit/debit card number, expiration date, verification code and billing address information) to process Platform-related payments. LMG does not itself store debit or credit card information on its servers. LMG offers Stripe as a third party payment processor to process purchases made through the Platform. Collected information is sent to Stripe which then sends us back a multi-use token that LMG stores on our servers. This token is unique to a specific card with a specific merchant, and ensures only LMG can ever use the token to process subsequent transactions. LMG utilizes this feature for a customer's convenience so you do not have to re-enter credit card information. For more information on its data collection and use practices of these payment processors, please review Stripe's Privacy Policy.
Marketing Services: We use MailChimp as our marketing platform for all marketing communications, such as our email newsletter. By subscribing, you acknowledge that your information will be transferred to MailChimp for processing. Learn more about MailChimp's privacy practices here.
Courier Services: LMG may use third party courier services to handle delivery or pickup of Customer Item(s). In order to utilize these services, LMG may release Customer contact information (e.g., email, phone, name) and addresses. We enter into contracts with such third parties regarding the services to ensure Personal Data is handled consistent with LMG's Privacy Policy and applicable law.
Anonymous Data – MixPanel Analytics: LMG utilizes MixPanel for tracking user-driven events such as how much time Users spend within our Platform, trends over time, and aggregate results across accounts. This information will be utilized by LMG to improve our Services. MixPanel collects information in accordance with its Privacy Policy. Users can opt-out of MixPanel's automatic retention of data collected by clicking here: MixPanel Opt-Out. If you get a new computer, install a new browser, erase or otherwise alter your browser's cookie file (including upgrading certain browsers) you may also clear the MixPanel opt-out cookie.
Sharing Services: Users may follow LMG and/or share information on social media sites such as Google, Facebook, Twitter, LinkedIn, Instagram, and Pinterest. Users who follow/share on such third party sites are subject to the data collection and privacy practices of such third party sites. Users should click on the applicable hyperlink for each share-service to review for more detail about information collected from these services. Users may choose to share information using social plug-ins provided by AddThis, their privacy policy is available here.
Third Party Services – Internal Use: We may share Personal Data with third parties who provide services on our behalf for purposes such as accounting, facilitating the exchange of data between LMG's employees, internal reporting purposes, etc. We enter into contracts with such third parties regarding the services to ensure Personal Data is handled consistent with LMG's Privacy Policy and applicable law.
Mandatory Disclosure of Sweepstakes Winner Information Upon Request: LMG is required, under applicable law, to provide to a list of winners' names for of any LMG sponsored sweepstakes to any third party who requests identification of such winners.
Other Potential Third Party Disclosures: Personal Data may also be disclosed to third parties to serve our legitimate business interests as follows: (1) as required by law, such as to comply with a subpoena, or similar legal process, (2) if LMG is involved in a merger, acquisition, or sale of all or a portion of its assets, (3) to investigate, prevent, or take action regarding suspected or actual illegal activities or to assist government enforcement agencies; (4) enforce our agreements with you, and/or (5) investigate and defend ourselves against any third-party claims or allegations. We will use commercially reasonable efforts to notify Users about law enforcement or court ordered requests for Personal Data unless otherwise prohibited by law.
3.	How Does LMG Comply With The Children's Online Privacy Protection Act and GDPR Regulations Relating to Children?
Only persons age 18 or older are authorized to establish an account or initiate an order. We do not knowingly collect Personal Data from anyone under the age of 18. If a parent or guardian becomes aware that his or her child (a) under the age of 16 in applicable EU Member Countries, or (b) under the age of 13 in the U.S. and applicable EU Member Countries, has provided us with Personal Data without parental consent, he or she should contact LMG at [email protected]. We will delete such Personal Data from our files within a commercially reasonable time, but no later than required under the applicable law relating the child's country of residence.
4.	How Long Does LMG Retain Personal Data Collected?
We will retain account and order data as long as it is necessary to facilitate Customer's use of the Platform and related services. Personal Data obtained from Site Visitors will be maintained as long as it is necessary to provide requested communications and information-based services or until a Visitor exercises its right to opt-out of requested communications or information-based services. Anonymized and Pseudo-anonymized data will be retained as long as LMG determines such data is commercially necessary for it legitimate business interests.
5.	EU General Data Protection Regulation ("GDPR") Notices
Data Controller. The information that we collect, process and/or use through the Platform is controlled by Catchbright, LLC., 3156 24th Street, San Francisco, CA 94110. Users may also contact us at any time by emailing us at [email protected].
We will only collect and process Personal Data about you where we have lawful bases. Lawful bases include consent (where you have given consent), contract (where processing is necessary for the performance of a contract for services with you), and "legitimate interests." Where we rely on your consent to process Personal Data, you have the right to withdraw or decline your consent at any time and where we rely on legitimate interests, you have the right to object. If you have any questions about the lawful bases upon which we collect and use your personal data, please contact us at [email protected].
Users within the EU may email LMG at [email protected] in order to exercise their GDPR rights to:
Access, review, restrict processing of, or otherwise request erasure of your Personal Data;
Obtain the identity of the source of any Personal Data collected;
Request correction of any errors contained within your Personal Data;
Request transfer your Personal Data to another service provider;
Object to the manner in which your Personal Data is processed; or
Lodge a complaint with a supervisory authority.
Where we rely on your consent to collect Personal Data, you may withdraw your consent either through the opt-out links provided in this Privacy Policy or through the contact information contained within this Section.
For all GDPR-based requests made pursuant to this section, LMG will (a) respond as required under applicable law, (b) provide a copy of any requested Personal Data in a structured, commonly used and machine-readable format, and (c) transmit such Personal Data to another service provider without restriction in accordance with applicable law.
6.	Transfer of Data to Servers in the United States
If you are located outside the United States and are visiting the Platform, you should be aware that Personal Data will be transferred to the United States, the laws of which may be deemed by your country of residence to have inadequate data protection. If you are located in a country outside the United States and voluntarily submit Personal Data to place an Order for any Item, such Personal Data shall be transferred to the United States for the legitimate interest of performing our contractual obligations to you. If you submit Personal Data to request information or subscribe to our newsletters, you explicitly consent to the general use of such information for marketing and informational purposes and to the transfer of that information to, and/or storage of that information in, the United States. All Personal Data transferred shall be collected and utilized in accordance with the terms of this Privacy Policy.
You may ask to review and correct the personal information that we maintain about you, or submit a complaint about our collection or use of your personal information, by sending a request to [email protected].
7.	Your California Privacy Rights
California law permits California-resident to request and obtain from LMG once a year, free of charge, certain information about their Personally Identifiable Information ("PII") (as defined by California law) disclosed to third parties for direct marketing purposes in the preceding calendar year (if any). If applicable, this information would include a list of the categories of PII that was shared and the names and addresses of all third parties with which we shared information in the immediately preceding calendar year.
We have implemented reasonable administrative, technical and physical security measures to protect your personal information against unauthorized access, destruction or alteration. LMG utilizes activity logs to identify any unusual activity, from authorized or unauthorized individuals accessing our systems or making changes to stored information. We regularly perform preventative system maintenance and monitoring to ensure the security of our data systems. However, although we endeavor to provide reasonable security for information we process and maintain, no security system can ever be 100% secure.
In addition, LMG utilizes a PCI-DSS compliant third party payment processor to ensure the security of Customer's Personal Data. Customers should review Stripe's Privacy Policy for more information on their security practices.
9.	How Does The Platform Respond To "Do Not Track" Signals?
"Do Not Track" is a feature enabled on some browsers that sends a signal to request that a website disable its tracking or cross-Platform user tracking. At present, the Platform does not respond to or alter its practices when a Do Not Track signal is received.
10. How Will I Be Notified Of Changes To Your Privacy Policy?
If we make material changes to our Privacy Policy, we will notify you by (1) changing the Effective Date at the top of the Privacy Policy, (ii) sending an email to all active account holders, and (iii) add a banner/notification to the Platform itself. Express consent will be obtained when required for any material changes in LMG's collection and use practices.
If you have any questions regarding your Personal Data or about our privacy practices, please contact us at: LMG, Attention: Privacy Department, 3156 24th Street, San Francisco, CA 94110 or at [email protected]
Customer questions: We do understand you'd like to speak to someone, as a small business, in order for us to keep up our low prices, we'd really appreciate your taking a few minutes to self-serve first! It's also faster, as our FAQs) can answer 90% of all questions & takes 2-3 minutes to review!
Text or call (listen for & press the correct key) +1-415-813-1881, 1pm to 8pm Pacific Time daily
Email [email protected], average ~24 hours response time
Existing orders: Most changes can be made from your order dashboard (see confirmation email) up to 24 hours before the start of your pickup time window. Otherwise, contact us as indicated above
Trouble with self-service access system only: call +1-415-813-1881 (listen for & press the correct key) anytime 24/7/365
Business inquiries: For partnerships, media inquiries, business development, or other inquiries, email [email protected]
Cover photo by Licensed by Creative Commons.


text:
Home Entertainment Sindh govt. came forward to rescue ailing Naila Jaffery
Sindh govt. came forward to rescue ailing Naila Jaffery
Lahore (Muhammad Yasir) Sindh Govt. announces financial support for senior actress Naila Jaffery who is suffering from cancer these days. Actress Naila Jaffery has been battling cancer for many years and is also facing financial difficulties these days. In this regard, she released a video a few days ago, she spoke about the plight and asked for financial help from senior actors. She had also said that in the past some royalties were paid in case of re-broadcasting of dramas on Pakistan Television Network. This is dire need to start it again as it will help the senior and sick actors like me a lot in overcoming the problems. After Naila Jafri's video came out, many artists came out in support of her. A close friend of Naila Jaffery also shared this video on Twitter in which she narrated the whole story of the actress which reached the Sindh government. After watching the video of Naila Jafri, the Minister of Culture Syed Sardar Ali Shah came forward and announced that all the expenses of the treatment of the actress would be borne by the Sindh Department of Culture. Indeed it is a great effort by Sindh govt. and Newsupdates Times will support it fully.
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We love this festive time of year when we can add some holiday decorations to our homes. However, there are ways we can do it without some of the tacky items, which are better left at the dollar store. We've racked our brains, and the great inter web, to bring you some fab Halloween decór ideas you'll want to leave up all year round.


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text:
Lo Lac d'Issarlés (oficialment Le Lac-d'Issarlès) és un municipi francès, situat al departament de l'Ardecha i a la regió d'Alvèrnia-Roine-Alps. L'any 2007 tenia 265 habitants.

Demografia

Població
El 2007 la població de fet de Le Lac-d'Issarlès era de 265 persones. Hi havia 104 famílies de les quals 32 eren unipersonals (24 homes vivint sols i 8 dones vivint soles), 44 parelles sense fills i 28 parelles amb fills.

La població ha evolucionat segons el següent gràfic:

Habitants censats

Habitatges
El 2007 hi havia 252 habitatges, 104 eren l'habitatge principal de la família, 132 eren segones residències i 16 estaven desocupats. 201 eren cases i 48 eren apartaments. Dels 104 habitatges principals, 80 estaven ocupats pels seus propietaris, 17 estaven llogats i ocupats pels llogaters i 7 estaven cedits a títol gratuït; 3 tenien una cambra, 8 en tenien dues, 17 en tenien tres, 34 en tenien quatre i 43 en tenien cinc o més. 79 habitatges disposaven pel capbaix d'una plaça de pàrquing. A 52 habitatges hi havia un automòbil i a 40 n'hi havia dos o més.

Piràmide de població
La piràmide de població per edats i sexe el 2009 era:

Economia
El 2007 la població en edat de treballar era de 151 persones, 101 eren actives i 50 eren inactives. De les 101 persones actives 92 estaven ocupades (54 homes i 38 dones) i 9 estaven aturades (8 homes i 1 dona). De les 50 persones inactives 28 estaven jubilades, 6 estaven estudiant i 16 estaven classificades com a «altres inactius».

Ingressos
El 2009 a Le Lac-d'Issarlès hi havia 92 unitats fiscals que integraven 192 persones, la mediana anual d'ingressos fiscals per persona era de 11.993 €.

Activitats econòmiques
Dels 20 establiments que hi havia el 2007, 1 era d'una empresa alimentària, 2 d'empreses de construcció, 6 d'empreses de comerç i reparació d'automòbils, 1 d'una empresa de transport, 8 d'empreses d'hostatgeria i restauració, 1 d'una empresa immobiliària i 1 d'una entitat de l'administració pública.

Dels 4 establiments de servei als particulars que hi havia el 2009, 1 era una fusteria, 2 restaurants i 1 agència immobiliària.

Dels 4 establiments comercials que hi havia el 2009, 1 era una botiga de més de 120 m², 1 una botiga de menys de 120 m² i 2 carnisseries.

L'any 2000 a Le Lac-d'Issarlès hi havia 17 explotacions agrícoles que ocupaven un total de 432 hectàrees.

Equipaments sanitaris i escolars
L'únic equipament sanitari que hi havia el 2009 era una ambulància.

El 2009 hi havia una escola elemental.

Poblacions més properes
El següent diagrama mostra les poblacions més properes.

Referències

 Résumé statistique Fitxa resum de dades estadístiques de Le Lac-d'Issarlès a l'INSEE.
 Évolution et structure de la population Fitxa amb el detall de dades de Le Lac-d'Issarlès a l'INSEE
 France par commune Dades detallades de tots els municipis de França accessibles a partir del mapa.

Municipis de l'Ardecha

redpajama_set_name: RedPajamaWikipedia


text:
Nick Liddi: Candidate for City Prosecutor
Nick Liddi: Running for City Prosecutor of Long Beach
Why are you interested in this position?
Long Beach is at a crossroads. The current City Prosecutor has failed to keep us safe. He has enriched himself year after year while allowing talented prosecutors to walk out his offices door. Low wages, a lack of interest in the work of his line deputies, and an ignorance of the actual courtroom where his prosecutors work tirelessly, is demoralizing, and dangerous. Every professional office needs a firm foundation, grounded in ethics, grit, compassion and understanding for all involved parties. This holds true especially for a prosecutorial office where inexperience can lead to mis-filings, mistrials, frustration of judges and defense attorneys, and can get junior prosecutors into hot water. This has a devastating effect on the public at large. Only concerned about his next paycheck and giving himself pay raises while criminals and street gangs are allowed to roam free. As your next City Prosecutor I'll take the same thoughtful and compassionate but tough on crime approach I have for over a decade as a prosecutor and now as a Los Angeles County Hardcore Gang Prosecutor and ensure there's a zero tolerance policy for street gangs. I'll also modernize the office, with a focus on retention, and ensure that our office prosecutors have the tools, training, and wages they need to succeed and keep you safe, keeping our office ethical and thoughtful. Each case is unique, and must be handled with care.
What relative experience do you have in this career field?
I worked as a prosecutor in the Long Beach City Prosecutors office years ago and now currently serve in the District Attorney's office where I am a hardcore gang prosecutor. I know what it take to clean the city up and keep families safe. This job requires the focus of a prosecutor, not a politician, to get the job done right.
What are 3 changes you would like to make while in office?
Crack down on crime by having a zero tolerance policy for street gangs.
Invest in crime prevention to stop crime before it starts.
No more endless pay raises for the elected City Prosecutor. Adequately pay, promote and train deputy city prosecutors to ensure we can recruit and keep the best prosecutors possible.
What are your top priorities for small businesses ?
In order for small businesses to thrive and grow they must be able to know that there businesses will be safe from street thugs and gangs. I will crack down on illegal street gangs and prioritize prosecuting crimes such as smash and grabs theft. I'll work with law enforcement to ensure that when an officer makes an arrest or writes a ticket that a qualified city prosecutor immediately follows through with the full force of the law.
What do you believe is the most important function of the City Prosecutor office?
To keep you safe. The job of the City Prosecutor is to ensure the our families and children are safe at work, playing in the park and at school. The current City Prosecutor has failed to do just that because he's been more interested in giving himself pay raises and chase cameras than prosecute criminals. Crime is on the rise and every part of our community is paying the price. I'll work tirelessly to crack down on illegal street gangs to ensure they can't go on to commit more violent crimes.
What are 2 key improvements or initiatives you wish to implement as City Prosecutor?
First, prioritize cracking down on violent street gangs.
Secondly, we have to solve homelessness. We must prioritize those who are living on the streets. It's a public safety issue. This requires a multipronged approach of addressing mental health, drug addiction and ensuring there is adequate housing and job training for those who need it the most.


Ali began riding as a young child. She joined a Bike User Group – Bike North in the late 1990's and has since been an active member.
Ali has cycled and camped around Tasmania, participated in a Cycling Challenge around Vietnam raising money for CARE Australia and completed a cycling tour around the South Island of New Zealand.
Ali has a Level 1 AustCycle Teacher Certificate, Cycle Skills Coach Certificate, Senior First Aid Certificate and a Working with Children Certificate. She has taught children how to ride, recreational bike skills and bicycle confidence courses.
Ali hopes to encourage others to share her passion and love of cycling.


text:
Q: Updating a CLOB XML in Oracle I have a CLOB column which contains a large amount of XML. I want to add a new attribute in that XML, like this attribute :
<name>me</name>

I tried using UpdateXML but I'm not getting it right.

A: CLOB is converted to XMLType using XMLType() and XMLType is converted to CLOB using to_clob. The following is an example.
create table table_with_clob (myclob clob);

insert into table_with_clob values ('<mytag><subtag>hello world</subtag></mytag>');

UPDATE table_with_clob SET myclob =
   to_clob(INSERTCHILDXML(xmltype(myclob),
   '/mytag', 'subtag',
   XMLType('<subtag>another</subtag>')));

select * from table_with_clob;

Output
myclob
------
<mytag><subtag>hello world</subtag><subtag>another</subtag></mytag>

Though I think this is not very efficient and you might better convert the column to XMLType and the operate with it.

redpajama_set_name: RedPajamaStackExchange


Setting Up Reporting Templates in Pulse—procedures to make the Co-browse templates available from Pulse.
Pulse Templates Overview—description of each Co-browse Pulse template.
Retrieved from "https://docs.genesys.com/Documentation:GCB:Deployment:PulseTemplates:8.5.0 (2019-04-24 11:07:51)"
This page was last modified on June 22, 2015, at 22:19.


text:
<?php

declare(strict_types=1);

namespace Centreon\Domain\Contact;

use Centreon\Domain\Contact\Exception\ContactServiceException;
use Centreon\Domain\Contact\Interfaces\ContactInterface;
use Centreon\Domain\Contact\Interfaces\ContactRepositoryInterface;
use Centreon\Domain\Contact\Interfaces\ContactServiceInterface;

class ContactService implements ContactServiceInterface
{
    /**
     * @param ContactRepositoryInterface $contactRepository
     */
    public function __construct(private ContactRepositoryInterface $contactRepository)
    {
    }

    /**
     * @inheritDoc
     */
    public function addUser(ContactInterface $contact): void
    {
    }

    /**
     * @inheritDoc
     */
    public function updateUser(ContactInterface $contact): void
    {
    }

    /**
     * @inheritDoc
     */
    public function findContact(int $id): ?ContactInterface
    {
        return $this->contactRepository->findById($id);
    }

    /**
     * @inheritDoc
     */
    public function exists(ContactInterface $contact): bool
    {
        $contact = $this->contactRepository->findById($contact->getId());
        return $contact !== null;
    }

    /**
     * @inheritDoc
     */
    public function findByName(string $name): ?ContactInterface
    {
        return $this->contactRepository->findByName($name);
    }

    /**
     * @inheritDoc
     */
    public function findBySession(string $session): ?ContactInterface
    {
        return $this->contactRepository->findBySession($session);
    }

    /**
     * @inheritDoc
     */
    public function findByAuthenticationToken(string $token): ?ContactInterface
    {
        try {
            return $this->contactRepository->findByAuthenticationToken($token);
        } catch (\Exception $ex) {
            throw ContactServiceException::errorWhileSearchingContact($ex);
        }
    }

    /**
     * @inheritDoc
     */
    public function findByEmail(string $email): ?ContactInterface
    {
        return $this->contactRepository->findByEmail($email);
    }
}

redpajama_set_name: RedPajamaGithub


MLS #1999872 Official listing information! Bella Collina neighborhood - 9634 Concord Rd located in Brentwood TN 37027, priced at $575000, with 0 bedrooms.
Land for sale in Brentwood, TN at 9634 Concord Rd. This land is priced at $275,120/acre.


text:
Cornelis August Wilhelm Hirschman (Medã, 16 de fevereiro de 1877 - Amesterdã, 26 de junho de 1951), conhecido como Carl Anton Wilhelm Hirschman, foi um banqueiro holandês, co-fundador da FIFA em 1904 e o segundo secretário geral da FIFA, servindo de 1906 a 1931. Em 1912, ele também foi um dos fundadores do Comitê Olímpico Holandês (NOC).

Quando o presidente da FIFA, Daniel Burley Woolfall, morreu em 1918, Hirschman impediu a organização de desmoronar, quase sozinha e às suas próprias custas, operando em seus escritórios em Amsterdam. Ele foi presidente interino da FIFA até Jules Rimet ser eleito seu terceiro presidente em março de 1921.

Após o crash de 1929, a empresa de negociação de ações de Hirschman faliu e o dinheiro que ele havia investido para o NOC e a FIFA ficou praticamente perdido. Hirschman renunciou inesperadamente ao NOC e à FIFA em 1931.

Mortos em 1951
Nascidos em 1877
Naturais de Medã
Banqueiros