Numerical Study On Several Kinds Of Asian Pricing Options

Nowadays,with the rapid flow of financial capital,people are still seeking ways to reduce risks while obtaining plum,the hedging of options is benefit for financial products,and many scholars have been attracted.There are many kinds of options,among which the Asian option stands out,the Asian option has low risk,it can meet the needs of investors.At present,most of the studies on Asian option pricing are based on the standard Brownian motion,and using variable substitution to become the heatconduction equation.But,there are the jump-diffusion process for the underlying asset price in the real financial market.So in this paper,the Asian option pricing under the Jump-diffusion and mixed Jump-diffusion model will be studied by using the radial basis function method(RBF,for short).This paper is organized as follows:(1)According to the no arbitrage principle and Ito formula,the option pricing of European call option under the Merton short rate model is obtained,and is studied by using RBF.The numerical experiment is carried out by using Matlab.The influence of the risk-free rate and volatility on the option value are simulated.(2)The model of the Asian pricing option with the jumping is obtained by using the Ito formula,the relevant properties of Brownian motion and Poisson distribution.By using new variables,this model is converted into nonlinear variable coefficient equation with two variables.Then using the RBF,the numerical solutions of this model is derived,and numerical results show the impact of volatility and jump intensity on Asian call and put option pricing.(3)By using Taylor expansion and self-financing dynamic strategy,the Asian option pricing model with dividend payments under mixed jump-diffusion model is obtained,the influences of the Hurst index and jumping strength on the option value are discussed by RBF.