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

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  • Emmanuel Coffie

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.

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  • Emmanuel Coffie, 2021. "Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations," Papers 2103.07651, arXiv.org, revised Jul 2021.
    • Handle: RePEc:arx:papers:2103.07651
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    References listed on IDEAS

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    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
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    4. Deng, Shounian & Fei, Chen & Fei, Weiyin & Mao, Xuerong, 2019. "Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
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    10. Bing‐Huei Lin & Shih‐Kuo Yeh, 1999. "Junp‐Diffusion Interest Rate Process: An Empirical Examination," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 26(7‐8), pages 967-995, September.
    11. Dung, Nguyen Tien, 2016. "Tail probabilities of solutions to a generalized Ait-Sahalia interest rate model," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 98-104.
    12. Brennan, Michael J. & Schwartz, Eduardo S., 1980. "Analyzing Convertible Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(4), pages 907-929, November.
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    Cited by:

    1. Emmanuel Coffie, 2021. "Numerical approximation of hybrid Poisson-jump Ait-Sahalia-type interest rate model with delay," Papers 2107.03712, arXiv.org, revised Jul 2021.

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