Grid design for improved CTMC convergence

Investigate grid design strategies for the CTMC state space of the short‑rate process that mitigate oscillatory convergence and enhance convergence rates in the CTMC approximation of zero‑coupon bond option and callable bond prices under time‑inhomogeneous short‑rate models such as Hull–White and CIR++.

Background

The numerical experiments reveal a sawtooth pattern (oscillatory behavior) in convergence when increasing the number of grid points. Prior work has shown that specific grid placements (e.g., positioning the strike midway between grid points) can reduce oscillations for other problems, but those techniques are not directly applicable to the present CTMC setup for interest rate derivatives.

The authors therefore highlight the need to develop new grid design methodologies tailored to CTMC approximations of interest rate models to improve numerical convergence.