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The GARCH option pricing model. (English) Zbl 0866.90031

Summary: 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.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91B84 Economic time series analysis
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References:

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