Barrier Option Pricing Problem

This paper is based on the suppose of continuous Black-Scholes model, by using the risk neutral pricing theory of option and analysising the distribution function of the first hitting time about the underlying asset value process, then achieve the pricing formula of barrier options, while the rate is constant, function of time t and stochastic respectively. Finally, we give the pricing formula of some double barrier options.Chapter one introduces some basic knowledge about option pricing, we achieve the pricing formulas for vanilla options, by using the risk neutral pricing method.Chapter two gives closed form formulas for single barrier options.Chapter three gives the approximated solutions (semi-explicitly) by using the Fortet's approximation when the rate and volatility is the function of timer. And while the barrier is discount, we can give the closed form formulas of single barrier options by using the Dambis ,Damlis&Scham theorem.Chapter four while the barrier is Vasicek, gives the approximated solutions for the barrier options, by using the measure changing and extended Fortet method. And while the barrier is discount, we give the closed form formulas for the barrier options, by using the Dambis, Dubins&Schwartz theorem.Chapter five gives the closed form formulas for some kinds of double barrier options.