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Zero Black-Derman-Toy Interest Rate Model

Grzegorz Krzyżanowski, Ernesto Mordecki and Andrés Sosa
The Journal of Fixed Income Winter 2022, jfi.2021.1.122; DOI: https://doi.org/10.3905/jfi.2021.1.122
Grzegorz Krzyżanowski
is on the faculty of Pure and Applied Mathematics in the Hugo Steinhaus Center at the Wroclaw University of Science and Technology in Wroclaw, Poland
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Ernesto Mordecki
is on the Facultad de Ciencias in the Centro de Matemática, at the Universidad de la República in Uruguay
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Andrés Sosa
is on the Facultad de Ciencias Económicas y de Administración in the Instituto de Estadística at the Universidad de la República Uruguay
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Abstract

We propose a modification of the classical Black-Derman-Toy (BDT) interest rate tree model, which includes the possibility of a jump with a small probability at each step to a practically zero interest rate. The corresponding BDT algorithms are consequently modified to calibrate the tree containing zero interest rate scenarios. This modification is motivated by the recent 2007–2008 crisis in the United States and it quantifies the risk of future crises in bond prices and derivatives. The proposed model can be useful to price derivatives. A comparison of option prices and implied volatilities on US Treasury bonds computed with both the proposed and the classical tree model is provided in six different scenarios along the different periods comprising the years 2002–2017.

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The Journal of Fixed Income: 32 (1)
The Journal of Fixed Income
Vol. 32, Issue 1
Summer 2022
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Zero Black-Derman-Toy Interest Rate Model
Grzegorz Krzyżanowski, Ernesto Mordecki, Andrés Sosa
The Journal of Fixed Income Nov 2021, jfi.2021.1.122; DOI: 10.3905/jfi.2021.1.122

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Zero Black-Derman-Toy Interest Rate Model
Grzegorz Krzyżanowski, Ernesto Mordecki, Andrés Sosa
The Journal of Fixed Income Nov 2021, jfi.2021.1.122; DOI: 10.3905/jfi.2021.1.122
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  • Article
    • Abstract
    • Different Approaches to Model the ZIRP
    • Our Proposal
    • THE BLACK-DERMAN-TOY MODEL
    • THE ZBDT MODEL
    • EMPIRICAL ANALYSIS OF DIFFERENT SCENARIOS WITH US TREASURY BONDS DATA
    • CONCLUSIONS
    • ACKNOWLEDGMENT
    • APPENDIX
    • REFERENCES
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