Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay

Coffie, Emmanuel and Mao, Xuerong (2021) Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay. Journal of Computational and Applied Mathematics, 383. 113137. ISSN 0377-0427

[img] Text (Coffie-Mao-JCAM-2020-Truncated-Euler-Maruyama-method-for-generalised-Ait-Sahalia-type-interest-rate)
Coffie_Mao_JCAM_2020_Truncated_Euler_Maruyama_method_for_generalised_Ait_Sahalia_type_interest_rate.pdf
Accepted Author Manuscript
Restricted to Repository staff only until 11 August 2021.
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo

Download (360kB) | Request a copy from the Strathclyde author

    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.