A COMPARISON OF DELTA HEDGING UNDER TWO PRICE DISTRIBUTION ASSUMPTIONS BY LIKELIHOOD RATIO

This paper compares net profits from delta hedging through the Delta of a European call option, by assuming underlying stock prices follows a geometric Brownian motion (GBM) or a Variance-Gamma (VG) process. We employ the maximum likelihood estimation method to estimate corresponding parameters for each process. A Monte Carlo simulation is conducted to simulate spot prices and option prices and a likelihood ratio (LR) method is used to estimate the Delta of the call option over different sample paths. We then implement a dynamic delta hedging strategy through the simulated spot prices, option prices and Delta at different hedging frequencies. Finally, we compare net profits calculated from hedging corresponding to a GBM or a VG process.