기하분수브라운운동을 가정한 옵션가격결정모형의 델타헤징 유용성

We investigate the improvement in the delta hedging of KOSPI 200 index options when fractional Brownian motion is taken into account. A fractional Brownian motion is a generalization of Brownian motion and the Hurst's parameter in fractional Brownian motion allows us to model the statistical long-range dependence of the underlying log returns. Specifically, Hu and Øksendal (2003)'s fractional option pricing model can reduce the impact of overfitting on hedging performance. Our empirical investigation leads to the following overall conclusions. Firstly, option’s delta calculated by implied information is better than the hedge-ratio from historical information. Secondly, regardless of information contents for parameter estimation, Hu and Øksendal (2003)'s fractional option pricing model outperforms the Black and Scholes(1973)’s model. Thirdly, the pair-wise comparison results among the models by bootstrapping test are significant and the empirical results by moneyness and sub-periods are very similar with those using all-sample. Finally, by reflecting additionally a non-normal distribution of an underlying log returns, the improvement over Hu and Øksendal (2003)'s model is expected.