Article1995

THE GARCH OPTION PRICING MODEL

1,131 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 article develops an option pricing model and its corresponding delta formula in the context of the generalized autoregressive conditional heteroskedastic (GARCH) asset return process. the development utilizes the locally risk‐neutral valuation relationship (LRNVR). the LRNVR is shown to hold under certain combinations of preference and distribution assumptions. the GARCH option pricing model is capable of reflecting the changes in the conditional volatility of the underlying asset in a parsimonious manner. Numerical analyses suggest that the GARCH model may be able to explain some well‐documented systematic biases associated with the Black‐Scholes model.

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References

1973The Pricing of Options and Corporate Liabilities 1986Generalized autoregressive conditional heteroskedasticity 1982Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1991Conditional Heteroskedasticity in Asset Returns: A New Approach 1993On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks 1973Theory of Rational Option Pricing 2005Theory of rational option pricing 1976Option pricing when underlying stock returns are discontinuous

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