Pricing Options In Jump Diffusion Models With Stochastic Interest Rate Using Mellin Transform

Many empirical studies show that the interest rate fluctuating over time has an important influence on the price change of options in the financial market,at the same time,the description of the emergence of emergencies in the financial market and their influence on the stock price is also an indispensable factor for an excellent pricing model.Based on the summary of previous research,this paper combines jump-diffusion process with stochastic interest rate to build a new pricing model of European options.Meanwhile,in recent years,many articles have shown that Mellin transform method can reduce the computational complexity compared with the traditional probability method,and is increasingly favored by scholars in option pricing practices.Based on this,we assume that the stock price obeys the geometric Brown motion,we first use the Mellin transform to obtain the form of the analytic solution of European options with fixed interest rate under jump-diffusion process.Then we loosen constraints,assume the interest rate follows Hull-White model.We also discuss the case when interest rate follows jump-diffusion process.By using the method of Mellin transform we get the pricing formula of European option under stochastic interest rate under jump-diffusion process.Through Mellin transform method,we can simplify the complex option pricing problem and get its solution,which provides a new method for option pricing research.The influence of the parameters on the option value is analyzed with a numerical example.