Some Research Results On Pricing Derivatives

Asian Option is the option of which the asset price at term relys on the average asset price. It has two benefits for using it. First, it can keep the value of the average price for the finance asset in a period of time. Second, it can avoid the risk by people who want to manipulate the asset price of option at term. So, Asian Option has been used abroad as a finance derive from tool. Another, the model on credit risk is a very important field in the finance research. In this paper, on the hypothesis of underlying asset price, enterprise value and enterprise debt following logarithmic normal processes, we researched the method of how to expand geometric average asian option to the default one with stochastic liabilities. By applying the method of structural approach, we derived the pricing formulas of default geometric average asian option with stochastic liabilities.Many experience distributing curves of the finance asset income exhibit the evidence phenomenon of decline and plump trail. It is different greatly from the traditional model of which the asset price obeys Geometric Brownian motion. In this thesis, based on the idea of jump and pervasion by Merton, we established a model for underlying asset price with a diffusion process involving jump and pervasion. By applying It(o|^)- Skorohod formula and martingale pricing sleight(risk neutral) within the framework of our model, we derived a closed form analytic solution for the pricing formulas of stock option with the rule of the biggest limit by rising and falling, and discussed its idiographic forms on the different circumstances by stochastic simulation and center limit theorem.