Questions tagged [volatility-smile]

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13
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2answers
2k views

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, ...
11
votes
6answers
2k 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 ...
9
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4answers
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 ...
8
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2answers
3k 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
719 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
votes
3answers
3k 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 ...
8
votes
1answer
621 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
5k 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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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 ...
7
votes
2answers
883 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
votes
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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1answer
5k 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
votes
1answer
748 views

Why do we fit volatility surfaces implied from a option pricing model to the empirical data?

As far as I understand volatility surface. It is made of 2 components, the volatility skew/smile and the volatility term structure. Together they form something like Implied volatility is ...
7
votes
2answers
876 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 ...
7
votes
1answer
299 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 ...
7
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0answers
610 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 ...
6
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1answer
1k 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\...
6
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4answers
3k 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
673 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 ...
6
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0answers
122 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\...
5
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1answer
100 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}(...
4
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4answers
1k 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 ...
4
votes
2answers
3k 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
300 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 "...
4
votes
1answer
818 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
votes
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
695 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
125 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 ...
4
votes
1answer
201 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
753 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=...
4
votes
1answer
915 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 ...
4
votes
1answer
486 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 ...
4
votes
1answer
390 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 ...
4
votes
1answer
195 views

Question about derivation of SABR volatility formula in original paper 'Managing Smile Risk' by Hagan et al

I have a question regarding the starting point of the derivation of SABR volatilities formulas in the appendix of the famous paper 'Managing Smile Risk' by Hagan et al. To derive SABR volatility ...
3
votes
1answer
534 views

Mixed local-stochastic volatility model in Quantlib

At a conference the speaker mentioned that it is a standard approach today to use a mix of local and stochastic volatility model in equity, FX and interest rates. Can you please suggest the most ...
3
votes
2answers
472 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 ...
3
votes
1answer
611 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
1k 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
390 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 ...
3
votes
1answer
389 views

Mixing Black Scholes with SABR

I am new to the whole concept of stochastic volatility so I am experimenting with option pricing. I think the concept is really difficult to understand / grasp. I was wondering if the following ...
3
votes
1answer
670 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 ...
3
votes
0answers
111 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 ...
2
votes
3answers
326 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.
2
votes
2answers
433 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 $...
2
votes
1answer
720 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
1answer
113 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 ...
2
votes
1answer
121 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 ...
2
votes
1answer
544 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 ...
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 ...