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

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Coffie, Emmanuel (2021) Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations. Preprint / 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.

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