Research On Barrier Option Valuation Driven By Levy Process

As one of the derivative securities, the option takes an important position in financial market for the last twenty years, it has been developing rapidly as an instrument for arbitrage,risk prevention and avoid more losses due to unfavorable price changes. Therefore, the importance of the option valuation in derivative securities and financial mathematics has never been overestimated.The Barrier Option is an exotic option whose payoff at expiry depends on asset price fluctuations during the option's lifetime. It can be classified as two classes:Knock out Option,when the price of the underlying asset arrives at a special barrier H, the option is out; the other is Knock in option, which only has effect when the price arrives at a barrier. Forward Option is a contract determined now but has payoff in the future. Combination with these two options, there will be a new option named Forward Barrier Option with both properties of those options mentioned above. This new option is main object for which we care in this thesis.This thesis mainly include two core conclusions: 1. In Black-Scholes Model, where all underlying asset price processes follow geometric Brownian motion with constant volatilities, the formula in closed form for European Forward Barrier call option valuation is given by martingale method. And the proof is given. 2. In Gaussian HJM framework, the formula in closed form for the valuation of European Forward Barrier call option on coupon bonds is given by forward measure approach in forward rate model. And the proof is given.