Delta Hedging Option Positions of the GARCH(11) and the Black-Scholes Models

Abstract

In this talk, we examine the delta hedging option positions derived from the Black-Scholes models and the GARCH(1,1) models, respectively, when the log returns of the underlying asset follows a GARCH(1,1) process. The implied volatility derived from the B-S model is shown to possess volatility smile property. The absolute values of the Black-Scholes deltas are proved to be higher than the GARCH (1,1)'s for deep out-of-money options, while are lower for deep in-the-money options, and are close for near-the-money options. Simulation study is also performed.