Questions tagged [volatility-smile]

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45 views

Difference of polynomial interpolation

I am using 5 volatility points to build a volatility smile : put 10D, put 25D, ATMF, call 25D and call 10D. I have thus 5 pairs of data : (Delta, Vol) let's say for example (10;5.75) ; (25; 5.50) ; (...
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44 views

is the concept of skew observed in fixed odds betting markets?

Bear with me if this sounds a little flippant, but this has got me curious. I know "sports arbitrage" is an active economic activity, although the arbitrage arguments, I think, are not ...
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1answer
62 views

Do single name stock option volatility surfaces exhibit steeper volatility smiles after stock price crash episodes?

In index options, there was not much of a smile (on the put-side) until the 1987 market crash. I'm wondering if the same applies to single name stocks? That is, do price crashes in individual stocks ...
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2answers
230 views

Black-Scholes: Volatility Smile “sharpens” with time to expiry

I have tried to calculate IV and log-moneyness (=log(S/K)) for different times to expiry (M = less than 1 month, Q = less than 1 quarter, S = less than 1/2 of an year, Y = less than 1 year, Y (+) = ...
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1answer
140 views

The most appropriate volatility model

Which would be the most appropriate models to find volatility trading opportunities (i.e. plot a theoretical volatility smile I can rely on) for the following instruments: Options on equity Options ...
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1answer
215 views

Bermudan Swaptions - Payer vs. Receiver (LGM)

There is abundant literature discussing the pricing of Bermudan swaptions and the relevance of single-factor Markov-functional models (e.g. LGM) versus multi-factor market models (e.g. LMM). From a ...
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1answer
167 views

Negative Density in Local Stochastic Volatility (LSV) Model Calibration

I'm trying to calibrate Local stochastic volatility model using finite difference method, and I'm mainly following this referece: Tian (2015). I met a problem when calibrating leverage function - the ...
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1answer
258 views

What is the difference between a volatility smile and a correlation smile?

I understand to plot correlation and volatility smiles, we have to plot the implied normal vol vs strike and observe a U-shaped relationship. How are these smiles different? Does a vol smile plotted ...
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2answers
135 views

Intuitive explanation for the value of a binary option being lower when volatility skew is positive?

According to the formula for pricing binary options with a volatility skew, it appears that the value of the binary option for a given strike gets lower, the higher the volatility skew at that strike. ...
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1answer
103 views

Can we observe smile arbitrage from the implied and local volatility?

Here are graphs of implied volatility and local volatility. Our prof mentioned that we can observe that the short end low strike region has some smile arbitrage. I would like to know how? Thanks
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How could option vega be remapped on reduced volatility surface?

try to be clear to ask my question: Suppose the original vol surface is a n by m matrix where n is the number of pillars in the volatility term structure and m is the number of strikes. According to ...
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1answer
135 views

Clean noisy data from arbitrage

My problem is that I have a surface of implied black volatilites that is supposed to represent market data. However, the surface contains some slight arbitrage. More precisely, the graph contains ...
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1answer
155 views

Relationship between time decay and gamma

In a paper titled Investing in Volatility published in 1998 by Emanuel Derman, Michael Kamal, Iraj Kani, John McClure, Cyrus Pirasteh, and Joseph Z. Zou, I found the following assertion (on page 9) ...
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1answer
146 views

Forward starting options concepts

Consider $t_0<t<T$, with $t_0=0$ (today date) and the standard payoff of a vanilla forward starting call option, $F_{t,T} = (S_T - S_t\cdot K)^+$, with strike $K$. If the price of this option is ...
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1answer
67 views

How does a concave up volatility smile correct high kurtosis for ATM option contracts?

Theoretically speaking, if we are to assume the following: Constant implied volatility throughout all strike prices The underlying's prices change distribution is log-leptokurtic and symmetric Then ...
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2answers
283 views

Question About SVI and SSVI Tradeoff between Fitness and No-Arbitrage

I’m currently working on a project to build a local volatility model out of implied volatility data and am struggling in the selection of an appropriate method to interpolate the volatility surface. I ...
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124 views

Angular bracket notation (physics)

In a few papers I have seen the following notation: $$ \langle X_t \rangle $$ Also, in Bergomi's book, at page 8, we have the following equality: $$ \biggr\langle \int_0^T e^{-rt}s^2 \frac{d^2P_{\hat{\...
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170 views

Hedging : effect of not matching the term structure of skew

Let us assume that we construct a pure stochastic volatility model calibrated to the implied volatility surface, but that the model does not replicate accurately the observed term structure of the ...
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2answers
203 views

Is the volatility smile a thing of the past?

Looking for example at this image from bloomberg of the OMX volatility surface, there is only a faint resemble of a smile at the shortest tenors that quickly dissipates as maturity is increased. I ...
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88 views

How does a volatility surface based on moneyness instead of strike stay consistent with put-call parity?

By definition due to put-call parity the implied volatility will be the same for puts and calls with the same strike price and time to maturity. Meanwhile, a volatility surface is often quoted in ...
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1answer
126 views

Expected Forward Volatility vs. Different Strikes

While theoretical options prices are derived from models, such as Black-Scholes, IV and IV skew reminds us that options prices are ultimately based on supply and demand. My question is the following: ...
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1answer
293 views

Interpreting SABR calibration model output

Calibrate a SABR model? Following on from this question, I have used the same market data they attached but am unsure on interpreting the output. When I plot the SABR probabilities against strike for ...
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1answer
80 views

Non-Trivial ATM Volatility in Vol smile construction from Market data on US Equities

have 2 quick questions please help. Constructing vol smile (OTM puts & OTM calls) from US equity market data. for Parabolas fit or other methods, the choice/method for ATM vol is non-trivial, ...
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36 views

How does the real market calculate the option prices when strikes are very small?

I'm working on the S&P500 European index options data(call options). On 2017-10-23, we have the closing price as 2564.98, and risk free rate is 1.09%(3 months treasury bill). If I choose the ...
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1answer
57 views

Trading butterfly a long vol or short vol [closed]

Sorry for what could be a naive question. When is the right time to trade a butterfly i.e. (buy 10d call and put vs sell atm all notional flat) is it when implied vols are high or low (relative to ...
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1answer
213 views

Implied Volatility vs Actual Volatility Calculation

To build a term structure I need different volatilities; as I don't get them at every strike, I use interpolation technique to calculate the rest and plot. This is how I calculate the implied vols. ...
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1answer
414 views

What does it mean that model can reflect the ”volatility smile”

I know that implied volatility is the value for which the Black Scholes model returns the correct option price. I also know that if we plot the volatility on the strike price chart, we will see "...
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1answer
207 views

Hedging a FVA in practice

A FVA (forward volatility agreement) is a forward contract on the ATM implied volatility. So at at maturity date $T$ the payoff of a FVA with unit notional is $$ (I_{ATM}(T,T') - K) $$ where $I_{ATM}(...
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2k views

Implied Vol Smile: from Calls, Puts or Both?

This might be a simple question, but I couldn't find the answer anywhere: is there a separate Volatility smile (and surface) based on Calls and a separate Volatility smile (surface) based on Puts? Or ...
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43 views

Terminology : definition of skew for a volatility smile

Is there a generally accepted definition of skew for volatility smiles? Is skew always defined as $$ \frac{\partial{\widehat{\sigma}(K,T)}}{\partial{K}}, $$ where $\hat{\sigma}:[0;+\infty)\times[0;+\...
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1answer
178 views

FX ATM-volatility quotes

Is the implied volatility ATM the same for a currency pair as for the inverted currency pair. I.e, can I expect the same volatility quote ATM for (for an instance) EURUSD as for USDEUR? And does this ...
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1answer
109 views

Do all stochastic volatility models capture volatility smile?

I started reading SABR model recently. In Wiki page, it states that the SABR model can capture volatility smile in derivative market. However, I do not see how it does so.
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200 views

FX Smile Polynomial Fitting

I am unable to reproduce the example of FX polynomial smile interpolation on page 59 of the book FX Option Pricing by Iain Clark shown below. Consider just the ATM volatility as a specific case. I ...
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1answer
302 views

Hedging vega risk with varswaps

I have encountered a statement that in summary reads like this: Varswaps became popular after the LTCM meltdown due to high levels of implied volatility the market was seeing at the time. Hedge funds ...
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1answer
91 views

When Fitting Implied Vol in, implied vol=ax²+bx+c, why is better to use moneyness than delta as independent variable?

I am trying to construct a smile curve using Option data, I can either interpolate implied vol vs delta or implied vol vs moneyness.
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2answers
128 views

A PARADOX? - relationship between risk reversal (slope of vol smile) and digital price

how do we resolve this seeming paradox? lets take GBPUSD now: it has a negative risk reversal, ie putvols > call vols , because traders expect spot to fall, so they are buying puts, pushing their ...
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2answers
2k views

Heston volatility surface in Python QuantLib

Does anyone have experience with the Python QuantLib function HestonBlackVolSurface? I'm trying to produce a 3D plot of the volatility surface as done in the ...
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1answer
306 views

Option Volatility Smile vs Delta

I am new to options trading and have been trying to better understand the relationship between implied volatility, delta, and moneyness. I was wondering how a call option's implied volatility can go ...
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1answer
235 views

Why SVI does not fit well short-maturity options?

As I understood, the SVI is widely used among practitioners. However, it is mentioned in many published papers (including ones written by Gatheral), that the SVI model does not fit well short-maturity ...
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2answers
1k views

How does volatility skew change with underlying spot?

We know that generally ATM implied vol is negatively correlated with the underlying spot for equity indices, i.e. implied vol goes up when spot moves down. Therefore I wonder if there are any ...
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0answers
82 views

Vol surface fitting with 5 degrees of freedom

For an options market making operation I need to be able to build a volatility surface, based on only 5 degrees of freedom, like e.g.: MaxPut, MaxCall, Skew, Curve and At The Money Vol. Is there an ...
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0answers
108 views

Hagan et. al original argument for SABR

In the original SABR paper (Hagan et al 2002 ), the introduction of the famous model is motivated by the observation that local volatility models spot dynamics work the wrong way. As the spot ...
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0answers
66 views

Extreme AUDJPY FX vols

I'm seeing levels of -12% of market strangle vol at 25 delta for AUDJPY at 20Y onward that is causing havoc with my pricing routines, the 10 delta market strangle is trading around -6% which is again ...
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3answers
470 views

Intuitive explanation for the smile in FX

What is the intuitive reason for the smile in FX? For equities this usually down to crash risk.
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1answer
246 views

Downward-sloping volatility skew in equity prices

I’m learning the market price for FRM, and I’m having a hard time understand a question in the assessment: From my understanding, the volatility skew for equity is the graph on the right upper corner:...
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0answers
222 views

Risk reversal basics and trading strategies

It it written in the book by Giles Jewitt: "If a currency pair had a completely flat volatility smile, the risk reversal strikes would be positioned approximately symmetrically around the ATM strike ...
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0answers
65 views

FX Smile Curve Extrapolation

How a smooth smile curve is generated from 5 smile points : 10D RR, 25D RR, 10D SM, 25D SM and ATM? What are the commonly used extrapolation and interpolation techniques? I have seen people ...
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1answer
185 views

FX smile extrapolation

Typically, 5 points data is available for smile construction : 25D RR, 25D SM, 10D RR, 10D SM and ATM. Questions: 1. How is a smooth smile curve generated with the help of these? 2. How is ...
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1answer
418 views

Smile Strangle and Market Strangle

What is the difference between Smile Strangle margin and Market Strangle Margin in fx derivative market? Is it just variation in convention or is there any mathematical relationship between the two?
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2answers
861 views

Why is the SVI parameterization in terms of variance?

The Gatheral SVI parameterization reads $$\sigma^2 = a + b \left[\rho(k-m) + \sqrt{(k-m)^2+s^2}\right]\,.$$ Why is it expressed in terms of variance $\sigma^2$ and not directly in terms of volatility $...