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

Coffie, Emmanuel (2021) Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations. Working paper. arXiv.org, Ithaca, N.Y..

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    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.