Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations

TL;DR

This paper analyzes a delay interest rate model with jumps, establishing strong convergence of numerical solutions using novel Euler-Maruyama techniques, aiding Monte Carlo calibration and valuation of financial instruments.

Contribution

It introduces new truncated Euler-Maruyama methods for delay interest rate models with jumps, proving their strong convergence under less restrictive conditions.

Findings

Strong convergence of numerical solutions demonstrated

Applicable to Monte Carlo calibration and valuation

New techniques handle non-explicit solutions

Abstract

In this paper, we study analytical properties of the solutions to the generalised delay Ait-Sahalia-type interest rate model with Poisson-driven jump. Since this model does not have explicit solution, we employ several new truncated Euler-Maruyama (EM) techniques to investigate finite time strong convergence theory of the numerical solutions under the local Lipschitz condition plus the Khasminskii-type condition. We justify the strong convergence result for Monte Carlo calibration and valuation of some debt and derivative instruments.