Numerical methods for jump-extended Cox-Ingersoll-Ross and constant elasticity of variance models

Abstract

The jump-extended Cox-Ingersoll-Ross (JCIR) model and jump-extended constant elasticity of variance (JCEV) model are stochastic differential equations (SDEs) used to forecast interest rates or stock prices. We simulate these SDEs directly by eight numerical methods: Euler Maruyama, simplified Euler, jump-adapted Euler, jump-adapted simplified Euler, jump-adapted order two weak, jump-adapted simplified order two weak, jump-adapted order two derivative free, and jump-adapted simplified order two derivative free. The transformed approach is also applied with these eight numerical methods. We compare their performance by testing the positivity preserving of numerical solutions, and finding their weak orders of convergence as well as their running time.