Strong convergence of Monte Carlo simulations of the mean-reverting square root process with jump

摘要

More and more empirical evidence shows that the jump-diffusion process is more appropriate to model an asset price, the interest rate and stochastic volatility. This paper considers the numerical methods of the mean-reverting square root process with jump. We concentrate on the Euler–Maruyama (EM) method and derive explicitly computable error bounds over finite time intervals. These error bounds imply strong convergence as the timestep tends to zero. We also prove strong convergence of error bounds under stochastic volatility with correlated jumps (SVCJ). Finally, we apply these convergence to examine some option prices and a bond.