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PRICING OPTIONS ON VARIANCE IN AFFINE STOCHASTIC VOLATILITY MODELS

Jan Kallsen · Johannes Muhle‐Karbe · Moritz Voß

43 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

We consider the pricing of options written on the quadratic variation of a given stock price process. Using the Laplace transform approach, we determine semi-explicit formulas in general affine models allowing for jumps, stochastic volatility, and the leverage effect. Moreover, we show that the joint dynamics of the underlying stock and a corresponding variance swap again are of affine form. Finally, we present a numerical example for the Barndorff-Nielsen and Shephard model with leverage. In particular, we study the effect of approximating the quadratic variation with its predictable compensator.

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References

2003Limit Theorems for Stochastic Processes 1996Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options 1999Option valuation using the fast Fourier transform 2001Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics 2003Affine processes and applications in finance 2003Stochastic Volatility for Lévy Processes 2003Lévy processes in finance pricing financial derivatives 2003Lévy Processes in Finance

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2018Closed-form variance swap prices under general affine GARCH models and their continuous-time limits 2021The Alpha‐Heston stochastic volatility model 2019A Gamma Ornstein-Uhlenbeck Model Driven by a Hawkes Process 2016Geometric Asian option pricing in general affine stochastic volatility models with jumps

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