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Stochastic Volatility
  • The Smile in Stochastic Volatility Models We consider general stochastic volatility models with no local volatility component and derive the general expression of the volatility smile at order two in volatility-of-volatility. We show how, at this order, the smile only depends on three dimensionless numbers whose precise expressions as functionals of the model's spot/variance and variance/variance covariance functions we provide. Finally we assess the accuracy of our order two expansion using realistic levels of volatility-of-volatility. , L.Bergomi, J.Guyon (2011)
  • Forward and Future Implied Volatility We address the problem of defining and calculating forward volatility implied by option prices when the underlying asset is driven by a stochastic volatility process. We examine alternative notions of forward implied volatility and the information required to extract these measures from the prices of European options at fixed maturities. We then specialize to the SABR model and show how the asymptotic expansion of the bivariate transition density in Wu {Wu10} allows calibration of the SABR model with piecewise constant parameters and calculation of forward volatility. We then investigate empirically whether current option prices at multiple maturities contain useful information in predicting future option prices and future implied volatility. We undertake this investigation using data on options on the euro-dollar, sterling-dollar, and dollar-yen exchange rates. We find that prices across maturities do indeed have predictive value. Moreover, we find that model-based forward volatility extracts this predicative information better than a standard "model-free'' measure of forward volatility and better than spot implied volatility. The enhancement to out-of-sample forecasting accuracy gained from model-based forward volatility is greatest at longer forecasting horizons. , P.Glasserman, Q.Wu (2010)
  • Prices Expansion in the Wishart Model Using probability change techniques introduced by Drimus for Heston model, we derive a n-th order expansion formula of Wishart option price in terms of Black-Scholes price and Black-Scholes Greeks. Numerical results are given for the second order case. Thanks to this new approximation, the smile implied by Wishart model can be better understood. The sensitivity of Delta and Vega to the volatility (respectively Vanna and Volga) indeed appear explicitly in this formula. En route to our formula, we present a number of new - to our knowledge - results on Laplace transforms and moments of the integrated Wishart processes. , P. Gauthier, D. Possamai (2009)
  • Smile Dynamics IV Smile Dynamics IVIn this paper we address the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. We introduce a new quantity, which we call the Skew Stickiness Ratio and show how, at order one in the volatility of volatility, it is linked to the rate at which the at-the-money-forward skew decays with maturity. We then focus on short maturity skews and (a) show that the difference between realized and implied SSR can be materialized as the P&L of an option strategy, (b) introduce the notion of realized skew. , L.Bergomi (2009)
  • Prices Expansion in the Wishart Model Using probability change techniques introduced by Drimus for Heston model, we derive a n-th order expansion formula of Wishart option price in terms of Black-Scholes price and Black-Scholes Greeks. Numerical results are given for the second order case. Thanks to this new approximation, the smile implied by Wishart model can be better understood. The sensitivity of Delta and Vega to the volatility (respectively Vanna and Volga) indeed appear explicitly in this formula. En route to our formula, we present a number of new - to our knowledge - results on Laplace transforms and moments of the integrated Wishart processes. , P. Gauthier, D. Possamai (2009)
  • Asymptotic Methods for Computing Implied Volatilities Under Stochastic Volatility , A.N.Medvedev (2008)
  • Stochastic Models of Implied Volatility Surfaces , R.Cont, V.Durrleman, J.Da Fonseca (2008)
  • Stochastic Local Volatility , C.Alexander, L.M.Nogueira (2008)
  • Risk Minimization in Stochastic Volatility Models: Model Risk and Empirical Performance , R.Poulsen, K.R.Schenk-Hoppe, C.O.Ewald (2008)
  • Lecture 10: Stochastic Volatility Models , E.Derman (2008)
  • Lecture 11: More on Stochastic Volatility Models of the Smile , E.Derman (2008)
  • Hyp Hyp Hooray , P.Jaeckel (2008)
  • Markovian Projection Method for Volatility Calibration , V. Piterbarg (2006)
  • Fast strong approximation Monte-Carlo schemes for stochastic volatility models , C.Kahl, P.Jaeckel (2006)
  • Stochastic Volatility for Real , J.Andreasen (2006)
  • A General Asymptotic Implied Volatility for Stochastic Volatility Models , P.Henry-Labordere (2005)
  • Moment Explosions in Stochastic Volatility Models , V. Piterbarg, L.Andersen (2005)
  • Stochastic Volatility Model with Time-dependent Skew , V. Piterbarg (2005)
  • Hedging Exotic Options in Stochastic Volatility and Jump Diffusion Models , K. Detlefsen (2005)
  • Arbitrage-Free Smoothing of the Implied Volatility Surface , M.R. Fengler (2005)
  • Local and Stochastic Volatility Models: An Investigation into the Pricing of Exotic Equity Options , L.Majmin (2005)
  • Exact Simulation of Stochastic Volatility and other Affine Jump Diffusion Processes , M.Broadie, O.Kaya (2004)
  • Mixture of Models: A Simple Recipe for a ... Hangover ? , V. Piterbarg (2003)
  • Lecture 1: Stochastic Volatility and Local Volatility , J.Gatheral (2002)
  • A Risk-Neutral Stochastic Volatility Model , Y. Zhu, M. Avellaneda (1997)





















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