Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 383, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cam.2020.113137
Keywords
Stochastic interest rate model; Delay volatility; Truncated EM scheme; Strong convergence; Monte Carlo scheme
Categories
Funding
- University of Strathclyde, UK
- Royal Society, UK [WM160014]
- Royal Society [NA160317]
- Newton Fund, UK [NA160317]
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This paper examines the analytical properties of the true solution of the Ait-Sahalia model with time-delayed volatility in the spot interest rate, and proposes new techniques for constructing numerical solutions. It is demonstrated that the truncated Euler-Maruyama approximate solution can be effectively utilized within a Monte Carlo scheme for valuing financial instruments such as options and bonds.
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. (C) 2020 Elsevier B.V. All rights reserved.
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