Baffle Option Pricing

Pricing barrier option is a very hot topic these days. In this thesis we discuss the problem of valuing barrier option on stock, and the barrier process is a stochastic process of the stock index. In detail, firstly by using Sharp Large Deviation we obtain the hitting probability expression; secondly we use Corrected Monte Carlo Simulation to simulate each path of the stochastic process of stock index, and use Antithetic Variable technique for every path and estimate cash flow; finally we discount the cash flow and get the option price, then the average of all prices of all paths is the barrier option price. Because Standard Monte Carlo simulations always give an over estimate of hitting time, we use Corrected Monte Carlo Simulation to estimate it. By comparing we find our method is correct and reasonable.