Discrete Time Hedging of OTC Options in a GARCH Environment: A Simulation Experiment

This paper examines the effect of using Black and Scholes formula for pricing and hedging options in a discrete time heteroskedastic environment. This is done by a simulation procedure where asset returns are generated from a GARCH (1,1)-t model. In the simulation a hypothetical trader writes an option and then delta- hedges his position until the option expires. It is shown that the variance of the returns on the hedged position is considerably higher in a GARCH (1,1) environment than in a homoskedastic environment. The variance of returns depends greatly on the level of kurtosis in the returns process and on the first-order autocorrelation in centered and squared returns.