Analysis of Hedging Profits under Two Stock Pricing Models

In this paper, we employ two stock pricing models: a Black-Scholes (BS) model and a Variance Gamma (VG) model, and apply the maximum likelihood method (MLE) to estimate corresponding parameters in each model. With the estimated parameters, we conduct Monte Carlo simulations to simulate spot prices and deltas of the European call option at different time spots over different sample paths. We focus on calculateing the deltas for the two models by the method of the infinitesimal perturbation analysis (IPA). Then, we employ dynamic delta hedging using the simulated spot prices and deltas for different hedging periods. Finally, hedging profits under these two models are calculated and analyzed.