An Empirical Approach of Delta Hedging in GARCH Model

In this paper, we compare the costs and efficiency arising from the delta-neutral dynamic hedging of options, using two possible values for the delta of the option. The first one is the traditional Black-Scholes delta, while the second one is the GARCH option pricing delta, namely the delta of the option in the generalized Black-Scholes model with a volatility calibrated from GARCH model. Both our theoretical analysis and empirical results of S&P 500 index options showed that single-factor version of the GARCH delta showed better performance than B-S delta (1973), especially when the volatility are very high. We believe the improvement is due largely to the ability of the GARCH model to describe the correlation of volatility with spot returns. This allows the GARCH model to capture strike-price biases in the Black-Scholes model that give rise to the skew in implied volatilities in the index options market.