Questions tagged [volatility-smile]

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Help needed in replicating FX Implied Vol Surface

I am relatively new to this area and am doing some self studying on SLV model. I am however getting stuck on trying to replicate this implied vol surface (which I will use to calculate the local vol) ...
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1 vote
1 answer
86 views

Deriving vol of vol from volatility futures price

From Colin Bennet's trading volatility (pg 117), he says: "A forward on a volatility future is short vol of vol. This means it is possible to back out the implied vol of vol from the price of ...
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Approximating SPX index skew using PutDex & CallDex

I hope someone can help me with this. As I don’t have access to historical options data I am wondering if it is possible to deduce SPX options skew from various volatility indices - in particular ...
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Vanna-Volga consistency result

In the Vanna-Volga (VV) paper by Castagna and Mercurio they state that, once you build up a curve of prices by interpolating-extrapolating on $K$, you can recover the same exact curve by redefining ...
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3 votes
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SABR LMM for RFR

Is there a research showing a way to use SABR LMM with new RFRs such as SOFR, i.e. pricing exotic path-dependent RFR derivatives with volatility smile and skew? I'm aware that Looking Forward to ...
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Market models of implied volatility and no arbitrage

Something has been bugging me for a while, and I can't really find an answer to it in papers. Maybe somebody can help me out. In addition to modelling the instantaneous vol, or modelling forward ...
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2 votes
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51 views

Expectation of Product of two European Option when vol smile exist

Currently I'm thinking about how to calculate the expectation of the product of two euro option, which is $E[(S_T-K_1)^+(S_T-K_2)^+]$ I can fit some parametric vol model from the market listed option ...
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"Back-Transforming" Smile Strangle into Market Strangle

I was wondering on whether FX vol experts here can comment on the following question: Suppose I have a properly stripped FX vol surface, which I constructed from ATMs and by market standard ...
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The relationship btwn RV-IV and realized skew

In studying skew I've been advised to focus on understanding on components that affect it. One such component that's been recommended to me is the relationship btwn RV-IV and realized skew. ...
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3 votes
1 answer
154 views

Calibration of a volatility smile model on a partial smile

I'm using a well-known SABR model in order to build an implied volatility surface of caps/floors on a very illiquid market which is entirely missing OTM quotes. What happens to SABR implied smile/...
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How to calculate the strike for a sticky delta volatility curve

I am sourcing the implied volatility for pricing the option. I am getting the volatility against delta but not the strike amount for those. How do I convert the delta into the strike to find the right ...
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147 views

Bloomberg OVML| FX option pricing | Python

Wanted to check if any API for python is available to replicate Bloomberg's OVML. The objective is to perform FX options pricing for multiple positions, and we are getting stuck in calculating ...
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1 answer
390 views

Pricing binary options under volatility smile

I was asked to show that the price of a digital/binary option $D$ while a volatility smile $\sigma(K)$ is present is given by $$D= \exp(-rT)( \Phi(d_2) - K \sqrt{T} \phi(d_2) \sigma ' (K))$$ Where $\...
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Can call price increase in falling markets

Say SPX falls so much that there is panic and implied volatility(iv) increases so greatly that OTM call prices are increased during the fall due to high iv In my observation in historical data this ...
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Clarity regarding Skew adjustment for binary options

I am reading the section on Skew adjustment for binary options on wikipedia (https://en.wikipedia.org/wiki/Binary_option#Skew) and am trying to get my head around it and gain some intuition. First ...
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Fitting a volatility smile with pySABR -- Python implementation of SABR model

In order to model some volatility smiles I'm using the python's pySABR package. I ran into a situation when I have two almost identical pieces of code for two different volatility smiles missing the ...
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Local volatilty models for fixed maturity curves with sparse equity data

I'm implementing an options analytics platform - with sparse market data going out a few months. Mostly equities and fx options. Building a fixed maturity curve like the one on quikstrike by bantix is ...
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1 answer
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Can't fit Bloomberg volatility smile with pysabr. What am I doing wrong?

I want to make sure that I can properly use SABR model on 1-period interest rate options, i.e. caplets, therefore I attempted to get lognormal volatilities for 4%, 6%, ATM, 8%, 10% strikes for 3Mx6M ...
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what is option zeta?

Is this an option greek? I've come across this term in some option book, and also online definition e.g. HERE: A measure that captures the premium difference between the value of an option calculated ...
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Why calibrate volatility Models to volatility surfaces rather than underlying's historical price data?

I'm trying to grasp the rationale for calibrating stochastic volatility models (i.e. Heston model) to empirical IV data from market prices. Doesn't this assume that the options are fairly priced and ...
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1 vote
1 answer
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How to extract volatility smile implied by a mixture model?

If one had to extract the implied volatility smile from a local volatility model, one can simply use the relationship: $\sigma^2_{imp}(t, x)T = \int_t^T \sigma^2_{loc}(s, x)ds$ with $\sigma_{loc}$ the ...
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1 answer
209 views

Difference of polynomial interpolation for volatility smile

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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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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2 votes
1 answer
70 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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6 votes
2 answers
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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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1 answer
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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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7 votes
1 answer
440 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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7 votes
1 answer
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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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2 votes
1 answer
319 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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4 votes
2 answers
272 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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4 votes
1 answer
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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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1 vote
1 answer
158 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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2 votes
1 answer
303 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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2 votes
1 answer
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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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1 vote
1 answer
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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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3 votes
2 answers
578 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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4 votes
0 answers
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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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6 votes
0 answers
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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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4 votes
2 answers
253 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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1 vote
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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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1 vote
1 answer
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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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1 vote
1 answer
621 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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1 vote
1 answer
118 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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0 votes
1 answer
86 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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0 votes
1 answer
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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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4 votes
1 answer
504 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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5 votes
1 answer
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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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9 votes
4 answers
3k 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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1 vote
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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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