Delay Ait-Sahalia-type interest rate model with jumps and its strong approximation-Reference-Cited by-同舟云学术

Delay Ait-Sahalia-type interest rate model with jumps and its strong approximation

Published:2023-07-01 Issue:3-4 Volume:40 Page:67-89
ISSN:2193-1402
Container-title:Statistics & Risk Modeling
language:en
Short-container-title:

Author:

Coffie Emmanuel¹

Affiliation:

1. Institute for Financial and Actuarial Mathematics , University of Liverpool , Liverpool , United Kingdom

Abstract

Abstract In this paper, we study the analytical properties of the true solution to the generalised delay Ait-Sahalia-type interest rate model with Poisson-driven jumps. Since this model does not have a closed-form solution, we employ several new truncated Euler-Maruyama (EM) techniques to investigate the finite-time strong convergence theory of the numerical solution 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.

Publisher

Walter de Gruyter GmbH

Subject

Statistics, Probability and Uncertainty,Modeling and Simulation,Statistics and Probability

Link

https://www.degruyter.com/document/doi/10.1515/strm-2022-0013/pdf

Reference22 articles.

1. Y. Ait-Sahalia, Testing continuous-time models of the spot interest rate, Rev. Financ. Stud. 9 (1996), no. 2, 385–426.

2. D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge Studies in Advanced Mathematics 116, Cambridge University, Cambridge, 2009.

3. M. Arriojas, Y. Hu, S.-E. Mohammed and G. Pap, A delayed Black and Scholes formula, Stoch. Anal. Appl. 25 (2007), no. 2, 471–492.

4. J. Bao, B. Böttcher, X. Mao and C. Yuan, Convergence rate of numerical solutions to SFDEs with jumps, J. Comput. Appl. Math. 236 (2011), no. 2, 119–131.

5. F. E. Benth, Option Theory with Stochastic Analysis: An Introduction to Mathematical Finance, Universitext, Springer, Berlin, 2003.

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