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Questions tagged [volatility-smile]

The tag has no usage guidance, but it has a tag wiki.

13
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2answers
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For which instruments performs SABR/LMM better than LMM?

For which class of instruments the SABR/LIBOR Market Model does perform better than the classical LIBOR Market Model? The LIBOR Market Model The LIBOR Market Model — also known as Brace, Gatarek, ...
9
votes
4answers
1k views

Why does the volatility smile flatten as maturities increase?

First, I can't find a purely "financial" explanation for this. Also the only mathematical explanation I've found so far was using the large deviations theory, which is quite complex. Is there a ...
8
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2answers
2k views

Arbitrage Free Volatility Smile

When ATM implied volatility is higher than OTM put and call I believe that the volatility smile is no longer arbitrage free? Why is that? On the other hand, when ATM implied volatility is lower than ...
8
votes
3answers
2k views

Concave volatility smile

Under what circumstances can implied volatility smile be concave (ATM implied volatility higher than OTM put and call)? I know that a slight concavity is not prohibited by no-arbitrage... What are ...
8
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2answers
532 views

In Dupire's paper, why is $(S_t, t)$ in the $(K, T)$ space?

I'm new to local volatility model. From Dupire's paper and most of the textbooks, they derived the local volatility $\sigma(K, T)$ in the $(K, T)$ (i.e., strike and maturity) space, from call prices ...
8
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1answer
497 views

Transforming 3M volatilities into 6M volatilities in EUR forecast curves

I have implemented a stripping algorithm to extract forward volatilities from cap/floor flat volatilities for different currencies. I am however struggling a bit when implementing a method to convert ...
7
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3answers
2k views

Forward implied volatility

Can one price accurately by only using vanilla options a derivative that is exposed/sensitive mainly to the forward volatility ? If it is impossible, why do we hear sometimes "being long a long ...
7
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2answers
548 views

Why is there greater demand for OTM and ITM options than for ATM options?

I´m currently writing a project on volatility trading and dynamics. The literature often states higher demand for OTM (out-of-the-money) and ITM (in-the-money) compared to ATM (at-the-money) options ...
7
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1answer
2k views

QuantLib: Black / BSM processes and pricing via volatility surface. Different results?

I start this question with a couple of C++ functions that will be useful to show some results. So start your Visual Studio C++ Express or Ceemple or whatever you want and copy & paste this: ...
7
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3answers
2k views

Variance swap replication and variance vega

Noob here. I've been trying to gain a better understanding of variance swaps and what better way than to replicate it with a portfolio of better understood instruments. I have read the GS 1999 ...
7
votes
1answer
4k views

SABR calibration: simple explanation and implementation

I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets. How would you explain the process and its implementation in simple steps? Any web ...
7
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1answer
164 views

How are the BKM risk-neutral moments derived?

I've been doing a lot of research on implied volatility skewness, and one of the most commonly cited papers I've come across is "Stock Return Characteristics, Skew Laws, and the Differential Pricing ...
6
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4answers
2k views

Volatility skew and how to capture it?

We see in the market that a implied volatility surface is not flat. Based on this observation different models were developed to capture the structure, e.g. CEV / SABR. A measure often used for the ...
6
votes
4answers
2k views

Downward sloping smile in normal model

We consider an stock price $S$ following a normal model: $dS_t = \sigma dW_t$ We can write this as $\frac{dS_t}{S_t}=\frac{\sigma}{S_t}dW_t$ Hence we can see that $S$ follows a "log-normal" ...
6
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2answers
634 views

Volar Higher Order Parametrizations

I came across this presentation from volar.io. The authors show fitting examples for a flexible volatility smile parametrization in 5 to 8 parameters which is also able to fit the locally concave ...
6
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0answers
76 views

Produce volatility smile/skew with G2++ model

Suppose I have a G2++ short rate model: $$r(t)=x(t)+y(t)+\phi(t), \quad r(0)=r_0$$ with $$dx(t)=-ax(t)dt+\sigma dW_1(t), \quad x(0)=0$$ $$dy(t)=-bx(t)dt+\eta dW_2(t), \quad y(0)=0$$ $$d\langle W_1,W_2\...
6
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0answers
171 views

Arbitrage free smoothing of volatility smile - cubic spline - implementation procedure

I am studying the paper Arbitrage-Free Smoothing of the Implied Volatility Surface, from Matthias R. Fengler (https://core.ac.uk/download/pdf/6978470.pdf). The problem I want to solve is much simpler ...
5
votes
1answer
419 views

SSR definition in Bergomi in relation to sticky strike and sticky delta

In Bergomi [Stochastic Vol Modelling] (Sec. 2.5.2), in the section on surface dynamics, the following definition of the "Skew Stickiness Ratio" (SSR) is made: $$ SSR = \dfrac{1}{\mathcal{S}_T}\frac{d\...
5
votes
2answers
437 views

Why is the volatility smile so important

This might seem like a dumb question. When using a volatility model, stochastic for example, we try to calibrate it so that it fits the implied volatility smile given by the market, but why is this ...
4
votes
2answers
656 views

Sticky Strike or Sticky Delta

Given market tick data for a single tenor for a futures and a set of options on the futures, how can I say if the IVs in the market at this point is sticky strike or sticky delta? I was trying to ...
4
votes
1answer
673 views

Is Cubic spline Interpolation on swaption Volatility arbitrage free?

If I use interpolation technique such as cubic spline to estimate volatility of Swaption with different strike,(with a given forward rate, swap and option maturity) will this be arbitrage free? What ...
4
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1answer
2k views

parameters in Heston model and their impact on volatility smile

Consider the Heston model given by the following set of stochastic differential equations: $$\frac{dS_{t}}{S_{t}}=\mu_{t}dt+\sqrt{V_{t}}dW_{t}, S_{0}>0,$$ $$dV_{t}=\kappa(\theta-V_{t})dt+\xi\sqrt{...
4
votes
1answer
474 views

Volatility Surface Constituents, do's and dont's

Recently I have been working a lot with implied volatility and volatility surfaces. The basic idea is easy to follow: 1) Gather market prices of options at different (Strike,Expiry) 2) Calculate ...
4
votes
1answer
131 views

Effect of Vol-of-Vol on VIX

What is the effect of vol-of-vol of an underlying on the VIX Index? The VIX is computed as hedging portfolio of log contracts to isolate pure volatility exposure without specifying an underlying ...
4
votes
1answer
543 views

What interpretation can I derive from an inverted volatility surface?

While pulling some reports from Bloomberg today I came across the volatility surface for NYSE: ONDK, set for an earnings call next Monday. From what I've seen before (not much, 1 month on the job and ...
3
votes
4answers
858 views

Trading spot volatility

I am reading a paper that very briefly talks about some volatility arbitrage strategies. It's so brief that I do not exactly understand how it works. It says one of the strategy is based on "short ...
3
votes
1answer
536 views

Why future (forward) volatility smile is important to path dependent option?

I was wondering why future volatility smile is important to path dependent option and American type option such as Bermudan swaption. It would be best if someone could provide a reference article as ...
3
votes
1answer
420 views

MTM Hedging Performance of Vanna-Volga

I was wondering how well Vanna-Volga (VV) Implied Vols "perform". So I experimented with the following option parameters $$S_0=100,\ K=92,\ r=0.03,\ q=0.01,\ T=2$$ and VV parameters $$K_1,K_2,K_3=...
3
votes
1answer
830 views

Spot and Vol Correlation in Idealised Regimes of the Volatility Surface

From http://www.globalvolatilitysummit.com/wp-content/uploads/2015/10/Santander-Volatility-Trading-Primer-Part-II.pdf it states that there are the four idealised regimes of volatility surface. 1) ...
3
votes
1answer
376 views

Shifted SABR for negative strikes

I am trying to apply SABR on EUR inflation caplets, with positive forward and negative strikes. Classical BS pricing is undefined, and so is SABR. I have read about the shifted SABR, which is supposed ...
3
votes
1answer
613 views

Why is the volatility smile important

One thing I can't understand clearly is why there is so much focus on the volatility smile. Given my knowledge of the Black and Scholes model, this is what I get: People use the volatility smile as a ...
2
votes
1answer
461 views

“Black-Scholes model implies flat implied volatility plots”?

I am a beginner in Finance and I get confused by the statement "Black-Scholes model implies flat implied volatility plots" Here is one form of this statement: (Dan Stefanica, 150 most frequently ...
2
votes
2answers
2k views

Vega hedging with implied volatility smile

I have a problem with vega hedging. Consider the management of an exotic derivative, such as Barrier option. Typically we do the following tasks: selecting a pricing model, say, a local volatility ...
2
votes
1answer
270 views

Effect of vol smile on risk neutral probability of ITM

I was asked in an interview about how the vol smile affect the price of a binary option, which is essentially the Prob(ITM) under risk neutral measure. My thought is that the implied vol at spot ...
2
votes
1answer
56 views

Literature on quoting vol surfaces in the absence of listed option prices [duplicate]

What are some of the modern methods used to price equity volatilities "the most accurately possible" when there are very few listed derivative prices available or even none at all? Do the pricers in ...
2
votes
1answer
331 views

SABR model: from calibration to mapping the smile/skew in a graph

Let's say that I have a calibrated SABR model in FX market (eg for Eurodollar options). So I have estimated values of beta, rho, alpha, and vol of vol. How do I map the calibration in a (strike, vol)-...
2
votes
1answer
239 views

What are some markets that don't have volatility smiles and why don't they?

I have read that volatility smiles didn't show up for equity options until 1987. Can some one give me an example(s) of what markets now still don't have volatility smiles and what an explanation for ...
2
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1answer
586 views

Some questions about implied volatilities and how to generate theoretical prices when market prices are not available

I am building a little Excel file that take some option prices in input and plots the volatility smile/surface. I have a script that reads market prices from the option chain for 3 different ...
2
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1answer
196 views

Why is the right part of the vol smile referred to as call skew

I often see the right part of the vol smile referred to as 'call skew'. However, due to put/call parity, this also represents skew for ITM puts. Is there a reason behind this convention?
2
votes
1answer
203 views

LSV model calibration with only few quotes per maturity

At this link I have asked what is the market standard when pricing options in different asset classes. Based on the answers, the standard for FX and equities seems to be the local-stochastic ...
2
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0answers
37 views

The Free Boundary SABR: Natural Extension to Negative Rates

In the paper by Antonov, Konikov and Spector An alternative approximation for the SABR model is presented. I'm interested to implement the formula for the ATM swaptions implied volatilities in the ...
2
votes
1answer
144 views

SSVI parametrization motivation , SSVI implementation

I've read the following paper of Gatheral and Jacquier https://arxiv.org/pdf/1204.0646.pdf about volatility surfaces. I'm thinking about the SSVI surface. Is there any motivation why they choose ...
2
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0answers
340 views

Vol surface changes as underlying moves

We market make in highly liquid, near term options markets. I want to build a risk report that tells us how our portfolio's greeks will change as the underlying moves. This is for risk management in ...
1
vote
3answers
447 views

At-the-money and volatility smile

In a volatility smile; why is the ATM point usually or ideally at the bottom? In other words, why is the "smile" smile shaped as opposed to another shape?
1
vote
2answers
228 views

How should I convert FX Volatility Surface from one base currency to another?

This might be a very simple question but I wanted to understand how to convert FX volatility surface points which are quoted in one base currency to another currency? Eg I have fx vol quoted in EUR ...
1
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2answers
76 views

Volatility smile shows individual Put and Call IV or combination

IV is calculated per strike AND option type basis(for example WTI 50 CALL its x and WTI 50 PUT its y). The question is when its shown in "Smile" its just shown on strike basis, so does that mean lower ...
1
vote
1answer
103 views

stochastic vol modelling not enough for smile

It seems in practice models that include Stochastic Volatility alone do not have enough power to produce actual observed implied vol surfaces. Is there recent empirical literature documenting this?
1
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1answer
380 views

Extrapolation of the volatility smile

Are there any market practices to extrapolate the volatility smile for equities? I already have an arbitrage free interpolated call prices data and I'm looking for a method to extrapolate beyond the ...
1
vote
1answer
244 views

On a FX volatility smile, Is a-delta put volatility equal to (1-a)-delta call volatility?

On a FX volatility smile in terms of delta, If I want 95-delta put vol, Is this volatility equal to a 5-delta call vol, and viceversa? Thanks.
1
vote
1answer
290 views

Mixture models of Stochastic Volatility and Local Volatility

As far as I can see on this website the stochastic volatilty models seem to be preferred to local volatility models, mainly due to the fact that stochastic volatility is 2D diffusive process whilst ...