Research On Asian Option Pricing Under Stochastic Interest Rate Subject To Subfractional Jump-Diffusion Process

With the increasing complexity of financial market,standard options have been difficult to meet special needs of customers,so financial institutions have designed many new options with flexible trading methods.Asian option is a representative and active new option,so it has important theoretical and practical significance for the Pricing of Asian option and other new options.In order to study the pricing of Asian option in the sub-fractional jump diffusion process of stochastic interest rate.First of all,the partial differential equation of price of Asian option and the initial boundary value condition,which is deduced by risk-free hedging theory and formula of ?Ito under the sub-fractional diffusion process or the sub-fractional jump diffusion process,then,the equation is transformed into the Cauchy problem of heat conduction equation by the variable substitution method,furthermore,the sub-fractional diffusion process or the sub-fractional jump diffusion process are further obtained from the classical solution formula of heat equation,finally,on the basis of the pricing formula,we use MATLAB software to further analyze stability of the pricing model of Asian options,such as Hurst index,zero interest bond,stock price,jump strength and other variables.The results show that Hurst index,zero interest bond,stock and jump intensity have significant influence on the price of Asian option.The Pricing model of Asian options in jump diffusion process under sub-fractional Vasicek model is more in line with actual financial market situation.The Asian option pricing problem studied in this paper can provide ideas and references for other new options pricing.