Article2006

APPROXIMATING GARCH‐JUMP MODELS, JUMP‐DIFFUSION PROCESSES, AND OPTION PRICING

Jin‐Chuan Duan · Peter H. Ritchken · Zhiqiang Sun

118 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

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset prices and volatilities. We extend theory developed by Nelson (1990) and Duan (1997) by considering the limiting models for our approximating GARCH Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffusion processes with correlated jump sizes. Convergence of a few GARCH models to their continuous time limits is evaluated and the benefits of the models explored.

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1976Option pricing when underlying stock returns are discontinuous 2016Numerical solution of stochastic differential equations 1987The Pricing of Options on Assets with Stochastic Volatilities 2000Transform Analysis and Asset Pricing for Affine Jump-diffusions 1997Empirical Performance of Alternative Option Pricing Models 2002The jump-risk premia implicit in options: evidence from an integrated time-series study 1991Stock Price Distributions with Stochastic Volatility: An Analytic Approach

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2010Tempered stable and tempered infinitely divisible GARCH models 2013Cojumps in stock prices: Empirical evidence 2009Volatility Components, Affine Restrictions, and Nonnormal Innovations 2008Option Valuation with Long-Run and Short-Run Volatility Components 2010Pricing and Inference with Mixtures of Conditionally Normal Processes

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