Mellin Transform Method Of Pricing Options Under Jump-Diffusion Model

With the development of global economy,there are more and more option types,which play important roles in the financial field.Jump-diffusion model can better explain the impact of emergencies on asset prices,and make the option pricing more in line with reality.The prices of options satisfy partial integro-differential equation under jump-diffusion model.Mellin transform is an effective method to solve partial integrodifferential equation without limiting the distribution of jump size.Moreover,it can simplify the pricing formula.Therefore,it is important to price options under jumpdiffusion model using Mellin transform.In this paper,we price exchange options and quanto options under jump-diffusion model using Mellin transform.The main contents are as follows:Firstly,we use Mellin transform to price the exchange options under the assumption that the processes of underlying asset prices follow jump-diffusion models.We first reduce the number of variables by change of variables and then derive the partial integrodifferential equations related to the prices of options using It?o-Doeblin formula.Then we obtain the pricing formula of exchange options using Mellin transform,which does not depend on the distribution of the jump size.Moreover,the accuracy of our pricing formula is verified by numerical example,and we also discuss the relationship between the price of exchange options and asset prices.Secondly,we use Mellin transform to price four types of quanto options under the assumption that the processes of underlying asset price and exchange rate follow jumpdiffusion models,the domestic and foreign riskless interest rates follow Vasicek models.We first derive the partial integro-differential equations related to the price processes of quanto options by the change of measure and It?o-Doeblin formula.Then we obtain the pricing formulas of quanto options using Mellin transform,which do not depend on the distribution of the jump size.In the end,the accuracy of pricing formulas is verified by numerical experiments,and we also discuss the relationships between the prices of quanto options and asset price or exchange rate.