Research On Stock Option Portfolio Based On Jump Brownian Motion

In order to research the portfolio problem of European Stock Option, we choose stock as its underlying asset and we suppose it obeys Brownian Motion with jump, we also use Mean-Variance Model and Mean-CVaR Model to measure its return and risk.However, it is difficult for us to calculate the mean and variance of our portfolio because the mapping between option price and the price of its delaying asset is nonlinear. So, we use Delta-Gamma method to get its approximation. Then, we can transfer the optimization problem of our portfolio to quadratic problemAt last, we choose the data from HKEx and get some empirical studies.