A Jump Diffusion Model With Stochastic Volatility And Stochastic Interest Rate And Convergence Of Its Numerical Solutions And Applications To Pricing Options

Asset price’s modeling in financial markets is an important part of the study offinancial mathematics. Many empirical studies have found that the volatility of anasset price is no long a constant, but satisfies a random process associated with theasset price, called stochastic volatility. In this paper, a more general jump model withstochastic volatility and stochastic interest rate is established. The stochastic volatilitymodel is a mean reversion process with an adjustable parameter γ. AnEuler-Maruyama numerical solution is given. And also it has been proved that thenumerical solutions of this model and related two common options converge to theircontinuous solutions in probability. At last, by means of a Monte Carlo simulationmethod，the simulation prices of two options are obtained.