Researching Arithmetic Average Asian Option Pricing By Binomial Tree And Trinomial Tree Approaching Method

To be one of the exotic options, the time to maturity function of Asian option depends on the average path of underlying asset in some periods. Usually, underlying asset arithmetic average price or geometric average price under predetermined time is the average price. As the most prevailing financial instrument in the market, Asian option under the assumption of following the geometric Brownian motion could only have, the only geometric average Asian option pricing has the explicit formula. The majority of underlying asset of Asian option are arithmetic average in the OTC market. Therefore researching Asian option pricing is becoming more significant. The binomial and trinomial tree approaches are visible and easily understanding, and are equivalent to the explicit difference method and are convergence to B-S model etc.First we discuss European and American option pricing by binomial and trinomial method and their convergence. Based on the Asian option pricing model and some common pricing methods, we separately introduce the European and American arithmetic average Asian option with binomial and trinomial tree approaches. Meanwhile, we proved the character of convergence of arithmetic average Asian option, and extend binomial Asian option pricing model to jump-diffusion situation, and provide the corresponding pricing model. The Last, we have application with numerical method and have analysis with its variables.