Pricing On Asian Option In Jump Diffusion Model

In recent years,as people gradually rising investment enthusiasm,the common one is European option and American option can not meet people's demand for investment,hence,a variety of exotic type options are derived from this demand and gradually attract lots of people's attention.Mostly in the exotic type options are path dependent options.Asian option is an option that path dependence,it's price is depend on the average path length.For this reason,Asian option is more stable than other option and is hard to manipulate.As for this reason it's very popular when it shows up.Asian option is an exotic option that depend on three asset,they are average asset,stock,dollar.According to the different average method and implement method,Asian option can be divided into different types.One of them is referent asset's geometric average Asian option,based on its good expression form,the features of easy to calculate,a lot of papers have been discussed its explicit solution of pricing formula and get the result.In the contrary,most papers discussed the solution of arithmetic average Asian option use the method of numerical simulation.But because the Asian option has the characteristics of path dependence,this make the Asian option pricing compared with common option is more complicated.This paper is focus on arithmetic average Asian option's pricing.This paper we adopt average asset,stock and bond as the three assets that Asian option depend on.Using every asset has its own martingale measure,Ito formula and Feyman-Kac formula,we can get simple form of partial differential equation under different referent asset,this simplification can make the formula that represent the price of Asian option satisfied more situation,in the same time,get more intuitive actual meaning.In the same time,we give detailed proof of partial differential equation in pure jump and jump diffusion model.In another way,we consider to expand the martingale of arithmetic average to geometric average,in order to get a simpler way and get intuitive form of the Asian option's price.