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Performance analysis of Zero Black-Derman-Toy interest rate model in catastrophic events: COVID-19 case study

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  • Grzegorz Krzy.zanowski
  • Andr'es Sosa

Abstract

In this paper we continue the research of our recent interest rate tree model called Zero Black-Derman-Toy (ZBDT) model, which includes the possibility of a jump at each step to a practically zero interest rate. This approach allows to better match to risk of financial slowdown caused by catastrophic events. We present how to valuate a wide range of financial derivatives for such a model. The classical Black-Derman-Toy (BDT) model and novel ZBDT model are described and analogies in their calibration methodology are established. Finally two cases of applications of the novel ZBDT model are introduced. The first of them is the hypothetical case of an S-shape term structure and decreasing volatility of yields. The second case is an application of the ZBDT model in the structure of United States sovereign bonds in the current $2020$ economic slowdown caused by the Coronavirus pandemic. The objective of this study is to understand the differences presented by the valuation in both models for different derivatives.

Suggested Citation

  • Grzegorz Krzy.zanowski & Andr'es Sosa, 2020. "Performance analysis of Zero Black-Derman-Toy interest rate model in catastrophic events: COVID-19 case study," Papers 2007.00705, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:2007.00705
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    References listed on IDEAS

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    1. Phelim Boyle & Ken Seng Tan & Weidong Tian, 2001. "Calibrating the Black-Derman-Toy model: some theoretical results," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(1), pages 27-48.
    2. Grzegorz Krzy.zanowski & Marcin Magdziarz & {L}ukasz P{l}ociniczak, 2019. "A weighted finite difference method for subdiffusive Black Scholes Model," Papers 1907.00297, arXiv.org, revised Apr 2020.
    3. Tian, Yingxu & Zhang, Haoyan, 2018. "Skew CIR process, conditional characteristic function, moments and bond pricing," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 230-238.
    4. Grzegorz Krzy.zanowski & Marcin Magdziarz, 2020. "A computational weighted finite difference method for American and barrier options in subdiffusive Black-Scholes model," Papers 2003.05358, arXiv.org, revised Dec 2020.
    5. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    6. Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2018. "Multiple curve L\'evy forward price model allowing for negative interest rates," Papers 1805.02605, arXiv.org.
    7. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    8. Frunza, Marius-Cristian, 2015. "Introduction to the Theories and Varieties of Modern Crime in Financial Markets," Elsevier Monographs, Elsevier, edition 1, number 9780128012215.
    9. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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