Study On Arithmetic Average Asian Options

Options are the most important financial derivatives, and they play an important role in risk management. Asian options are the most actively trading exotic options, the research of Asian options has attracted widespread attention. Because there is no analytical solution for arithmetic average Asian options, a new kind of method called numerical methods is needed in our paper. The usual binomial tree model is popular in option pricing because of its intuitive, simple and practical, and it has a good effect for various option pricing.This paper mostly studied that using the new binomial tree parameter model to price discrete arithmetic average Asian options in the risk-neutral world. First, we introduce the classical Black-Scholes option pricing model, and give some comments about the problems of this model; Second, for the defects of the usual binomial tree model, a new type of binomial tree parameter model is constructed, and it has more high calculating accuracy and convergence than the original binomial tree model in the European options pricing; Moreover, we introduce the basic knowledge and theory of the Asian option pricing ,and give a brief for the situation of geometric average Asian options and arithmetic average Asian options; Finally, the discrete arithmetic average Asian options are studied by using the new binomial tree parameter model, in this new model, the bisection method is used to select the representative averages, and calculate the price of options by linear interpolation law. The numerical results show that the new binomial tree parameter model is more effective than the original model for the arithmetic average Asian option pricing, and has better property in accuracy and convergence.