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

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.

arXiv commentarXiv admin note: text overlap with arXiv:2107.03712

References in corpus (2)

• The Truncated Euler-Maruyama Method for Stochastic Differential Delay Equations
• Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation