Reset Options Model With Random Time

It is a inevasible trend to establish new and more option models with the rapid development of economy and the investment demand. So,a lot of domestic and abroad scholars put forward many option models such as default risk valuation model,reset options model,jump-diffusion model and so on.Basing on the analysis of those models,this paper studies the default risk valuation model,investigates reset option with random time. The resets option means that the option taker can reset the premium at any time with paying a certain amount of default to the option writer. And the reset of the strike price and the amount of default money should be decided both by the taker and writer. Assuming the liner relation between the default money and the strike price,and that default money is a function of time. At last,the paper derivates the pricing formula of European call option by using equivalent measure transformation and martingale methods for two cases: one is consider of stock price, the other is consider of the price of foreign exchange market.