Truncated Euler-Maruyama method for generalised Ait-Sahalia-type interest rate model with delay

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Abstract

The original Ait-Sahalia model of the spot interest rate proposed by Ait-Sahalia assumes constant volatility. As supported by several empirical studies, volatility is never constant in most financial markets. From application viewpoint, it is important we generalise the Ait-Sahalia model to incorporate volatility as a function of delay in the spot rate. In this paper, we study analytical properties for the true solution of this model and construct several new techniques of the truncated Euler-Maruyama (EM) method to study properties of the numerical solutions under the local Lipschitz condition plus Khasminskii-type condition. Finally, we justify that the truncated EM approximate solution can be used within a Monte Carlo scheme for numerical valuations of some financial instruments such as options and bonds.
Original languageEnglish
JournalJournal of Computational and Applied Mathematics
Publication statusAccepted/In press - 1 Aug 2020

Keywords

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

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