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

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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.
Original languageEnglish
Place of PublicationIthaca, N.Y.
Number of pages27
Publication statusPublished - 13 Mar 2021

Keywords

  • stochastic interest rate model
  • delay volatility
  • Poisson jump
  • truncated EM scheme
  • strong convergence
  • Monte Carlo scheme

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