High order splitting schemes with complex timesteps and their application in mathematical finance

TL;DR

This paper develops high order splitting schemes with complex timesteps for solving Kolmogorov backward equations, demonstrating their robustness and effectiveness in interest rate models like CIR2.

Contribution

It introduces high order splitting schemes with complex timesteps and proves their analyticity in weighted spaces, applying them to financial models.

Findings

Numerical results confirm robustness in drift-dominated problems.

The schemes are effective for Kolmogorov backward equations in finance.

Theoretical proofs establish analyticity of split semigroups.

Abstract

High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in Stratonovich form. In the setting of weighted spaces, the necessary analyticity of the split semigroups can be easily proved. A numerical example from interest rate theory, the CIR2 model, is considered. The numerical results are robust for drift-dominated problems, and confirm our theoretical results.