Asian Option Pricing With Volatility Following A Finite Markov Chain

Since 1970s, the rise of modern financial derivatives is one of the most dramatic changes occurring in the global financial field. As the core of the financial derivatives, option has became the emphasis and hotspot which the theorists research. And one of the theoretical researches of the option has focused primarily on how to price options.Asian option is one of the most active exotic options in the financial derivatives market. Its terminal payoff is not only connected with the price of underlying asset on the expiration date, but also depends on average price over a part or the whole of the life of the options. For the price of Asian options lies on its average price, so it can avoid the possibility of the investor manipulate the price near the end of period to get sudden huge profit.In traditional option pricing method the volatility is assumed as a constant, but this is contradicted to the fact. According to practice, many models for stochastic volatility were presented, such as Stochastic Volatility model(S—V model), GARCH model. However the pricing using these volatility models are very complex, and we usually cannot get its exactly solution, even numerical solution. Aimed at this case, this paper try to construct a simple stochastic volatility model— volatility following a finite Markov chain. On one hand this model acts in accord with the stochastic of volatility, on the other hand avoids the pricing difficulty of common ways.This paper consists in two following works: l.The pricing of continuous average Asian option in the model which volatility following a finite continuous parameter Markov chain is put;2.Aimed at the complex pricing of Asian option in continuous parameter Markov chain model, so we consider the model which volatility following a finite discrete parameter Markov chain, and we get the price of discrete average Asian option in discrete parameter Markov chain model which is similar to the price in continuous parameter model. And finally a numerical case in discrete parameter model is put.