GARCH Gamma
JOURNAL OF DERIVATIVES Vol 2 No 4
Posted: 10 Oct 1998
There are 2 versions of this paper
GARCH Gamma
Abstract
This article addresses the issue of hedging options positions when the underlying asset exhibits stochastic volatility. By parameterizing the volatility process as GARCH, and utilizing risk-neutral valuation, we approximate hedging parameters (delta and gamma) using Monte Carlo simulation. We estimate hedging parameters for options on the Standard & Poor's 500 index, a bond futures index, a weighted foreign exchange rate index, and an oil futures index.We find that Black-Scholes and GARCH deltas are similar for all the options considered, while GARCH gammas are significantly higher than BS gammas for all options. For near-the-money options, GARCH gamma hedge ratios are higher than BS hedge ratios when hedging a long-term option with a short-term option. Away from the money, GARCH gamma hedge ratios are lower than BS.
JEL Classification: G13
Suggested Citation: Suggested Citation