Article2004

GARCH and Volatility swaps

Alireza Javaheri · Paul Wilmott · Espen Gaarder Haug

77 citations0/0 files storedQuantitative Finance

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

Abstract

This article discusses the valuation and hedging of volatility swaps within the frame of a GARCH (1, 1) stochastic volatility model. First we use a general and flexible partial differential equation (PDE) approach to determine the first two moments of the realized variance in a continuous or discrete context. Next, and also the main contribution of the paper, is a closed-form approximate solution for the so-called convexity correction, when the risk-neutral process for the instantaneous variance is a continuous time limit of a GARCH (1, 1) model. Following this, we provide a numerical example using S&P 500 data.

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References

1987The Pricing of Options on Assets with Stochastic Volatilities 1993Measuring and Testing the Impact of News on Volatility 1990ARCH models as diffusion approximations 2010Towards a Theory of Volatility Trading 1997The Complete Guide to Option Pricing Formulas 2006Paul Wilmott on Quantitative Finance 1999Pricing Options under Generalized GARCH and Stochastic Volatility Processes 1988A Simple Formula to Compute the Implied Standard Deviation

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