Numerical methods for jump-extended cox-ingersoll-ross and constant elasticity of variance models

Abstract

The jump-extended Cox-Ingersoll-Ross and jump-extended constant elasticity of variance models are stochastic differential equations (SDEs) used to forecast interest rates or stock prices. We simulate these SDEs directly by eight numerical methods: Euler Maruyama method, simplified Euler method, jump-adapted Euler method, jumpadapted simplified Euler method, jump-adapted order two weak method, jump-adapted simplified order two weak method, jump-adapted order two derivative free method and jump-adapted simplified order two derivative free method. 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 run time.