Continuous-Martingale Analysis In Option Pricing

Financial organizations will face many kinds of financial risk in investment. If not careful,they will have great losses, sometimes may go bankrupt. As a result, how to measure and elude financial risk is a importent problem financial organizations want to solve as soon as possible. Option is one of the most powerful tools to elude financial risk and hedge, so it is of real significance to study option-pricing theory. Meanwhile, continuous-martingale analysis is one of the most powerful tools in option-pricing theory. Thus it is also of theorical and real significance to apply it to pricing options.At first, the paper reviews the development of the option-pricing theory and summarizes its foundation. Then the paper generalizes the theory of continuous-martingale analysis and introduces the application of the theory to the fundamental theorems of asset pricing. On this basis, the paper mainly proves that the value process {V(t TL H,S );0 t T} of European continuous-timeknock-out double-barrier put option is a martingale in the complete market without transaction costs, and the martingale property of single-barrier put option is given. At the same time, the pricing problem of American knock-out double-barrier put option is also being discussed, and the formula for determining its value at any time t(0 t T) is obtained.