Research On Solution And Application Of Asian Option Pricing Model Based On Finite Volume Method

A large number of new options are derived from the modern international financial market.These options are path dependent,among which the most active Asian options are typical.There are two types of Asian options: Geometric Average Asian option and arithmetic average Asian option.At present,geometric average Asian option can be calculated by explicit pricing formula.However,due to the asset price after arithmetic average no longer obeys lognormal distribution,it can not get analytical solution,and only can seek approximate pricing method as close to the real result as possible.Therefore,it is of great academic value to study the approximate solution of arithmetic average Asian option pricing model by using numerical method.The thesis studies the pricing of Asian options from the following two aspects:In the first place,the author present a simple and efficient finite volume method governing arithmetic average Asian option pricing.In the thesis,firstly,the arithmetic average Asian option pricing model is transformed into a conservative form,and the finite volume method is used to solve the model based on a fitted finite volume spatial discretization and an implicit time stepping technique.Secondly,the iterative steps in the discretization process are summarized to solve the discrete equations,and the positive definite proof is carried out after the transformation to the matrix form to ensure the correctness of the solution;Finally,the results of finite volume method are compared with those of binary tree method and Monte Carlo method to verify the effectiveness and practicability of the method.In the second place,based on the finite volume method,the thesis analyzes the pricing of Shanghai 50 ETF options.Based on the finite volume method,the thesis makes an empirical analysis of Shanghai Stock Exchange 50 ETF options from two aspects.One is to compare the difference between the theoretical price and the actual transaction price of European option pricing model,and analyze the reasons for the difference.The other is to calculate the Asian option price of the Shanghai Stock Exchange 50 ETF option,and compare the result with the European option theory price,and analyze the applicability of the two in China's market.The results show that the finite volume method is correct and effective in governing the Asian option pricing model,and they show good adaptability in many situations.The theoretical price and the actual transaction price of European option pricing model based on this method are highly consistent.For the same option product,the Asian option price is not only lower than the European option level,but also is not easily affected by the underlying asset price volatility,which can reduce the risk of market price volatility.Compared with European options,Asian options are more suitable for the development of China's financial market at this stage.