THE GARCH OPTION PRICING MODEL

Jin‐Chuan Duan

Mathematical Finance · 1995 · 1.2K citations · 30 references

Concepts

TL;DR

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.

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.

References

30