An Approximate Algorithm For Asian Option Pricing

Asian option is one of the most active exotic options in the financial derivatives market. Different from standard option, its benefit is related to the average price of underlying asset in the valid period of the options. Asian option has many merits, for instance the price is relatively cheap and has low risk and so on. Because Asian option can effectively prevent the underlying asset price being manipulated, it is welcomed by Investors. Its pricing problem has also become a hot of research recently.According to the different average meanings, Asian option can be divided into geometric average Asian option and arithmetic average Asian option. For the geometric average Asian option, it has a closed form solution for the option price with the classical Black-Scholes model, the reason is that the price of underlying asset follows the log-normal distribution,the geometric average of a series of log-normal distribution random variables still follow the log-normal distribution. For the arithmetic average Asian option,it does not has a closed form solution for the option price with the classical Black-Scholes model, because the arithmetic average of a series of log-normal distribution random variables don't follow the log-normal distribution.In this paper, we mainly study the pricing problem of Asian options in the discrete model, and discuss the pricing of geometric average Asian options and the pricing of arithmetic average Asian options with the CRR model. Because Asian option have a strong dependenceon the path, when the number of time steps is increasing, the number of paths increases exponentially,it causes enormous computation. In order to solve this problem, we classify all the paths to same node with the "k method".According to thisclassification method, it is easy to get the recurrence relation of the maximum value of each kind of path and the recurrence relation of the minimum value of each kind of path. Then through these representative mean, we uselinear interpolation method, the risk neutral pricing theory and backward recursive methodto compute the upper and lower bounds of the price of arithmetic average Asian option. For the n step of the binomial tree,the time complexity of the algorithm for the estimation is O(n4). Finally, we use ourmethod to simulate the pricing of Asian option, and the results show that when the number of time steps increases, the price of Asian option is more and more accurate, and the method is feasible.