Mathematical Finance · 1995 · 1.2K citations · 30 references
BusinessEconomicsFinanceEconometricsFinancial EconometricsFinancial EconomicsAsset Pricing EmpiricsAsset Pricing TheoryAsset Return ModelingOption PricingOption Pricing ModelsVolatility ModelingArch ModelsAsset VolatilityBiasesBlack-scholes ModelGeneralized Autoregressive Conditional Heteroskedasticity ModelsOption Pricing TheoryTime-varying Volatility ModelsVolatility
The article develops an option pricing model and its delta formula for assets following a GARCH process. The model is derived using the locally risk‑neutral valuation relationship (LRNVR). Under specific preference and distribution assumptions the LRNVR holds, and the resulting GARCH option pricing model captures conditional volatility changes parsimoniously, with numerical tests suggesting it can explain systematic biases of the Black‑Scholes model.
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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The Pricing of Options and Corporate Liabilities
Fischer Black, Myron S. Scholes · Journal of Political Economy · 1973 · 29.4K citations
Generalized autoregressive conditional heteroskedasticity
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