Asian Option Pricing And Hedging

The development of financial derivatives is a new melody in the international financial fields since the 1980's .As the core of financial derivatives, option becomes emphases of studying in theory and practice , above all it must be solved that how to price option and hedge risk.In this article, the author studies the option pricing and hedging by the martingale method. Firstly, the principle of option pricing was introduced , based on the pricing and hedging of European option under the frame of Black- Scholes model , this paper proceeds two aspects: on the one hand, Asian option has the strong path dependence, pricing is very complicated, by change of numeraire and measue, this paper gives a handy solving process of Asian option with geometric average striking price, and gets an ideal price and hedging strategy ; On the other hand , the pricing and hedging of Asian option under stochastic volatility model are discussed , first to prove the market completion ,on this basis ,the paper gets a common formula and approximate solutions by the martingale method.