On Asian Option Pricing For Generalized Model Of Black-Scholes Model

This paper is concerned with the pricing of arithmetic average Asian options. In the celebrated B-S model, the underlying asset is continuous-time and volatility and riskless are constants , hence a closed form solution for the pricing problem is given. But in fact , empirical studies show that some great events can lead to brusque variations in price , namely Asian option with jumps and empirical study has proved that volatility is not constant in general. So we need to modify the B-S model so that it conforms to the reality situation at first.We mainly discuss two generalized models: Which one is that the volatility is assumed to be stochastic and the price of the underlying asset is driven by Brown motion , so that we can propose a new generalized model of the B-S model; The other is that the volatility is assumed to be stochastic and the price of the underlying asset is a Lévy process, namely we can further promote the model on the basis of the first one . Then we assume that the price of the underlying asset subjects to the two models respectively , and derive the obvious formula or upper bounds for arithmetic average Asian option prices.