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Black-Scholes and Heston Models with Stochastic Interest Rates and Term Structure of Volatilities

Alberto Bueno-Guerrero
The Journal of Derivatives Fall 2019, jod.2019.1.078; DOI: https://doi.org/10.3905/jod.2019.1.078
Alberto Bueno-Guerrero
is an economics teacher at IES Francisco Ayala in Granada, Spain
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Abstract

We consider the Black-Scholes and Heston models and generalize them to stochastic interest rates and maturity-dependent volatilities. In the Black-Scholes case, we solve the extended model and provide a concrete form for the term structure of volatilities. In the Heston case, we prove that, under some conditions, the generalized model is equivalent to a hybrid model and we find semi-closed-form solutions in the Hull and White and CIR cases.

TOPICS: Options, statistical methods, fixed income and structured finance

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The Journal of Derivatives: 28 (2)
The Journal of Derivatives
Vol. 28, Issue 2
Winter 2020
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Black-Scholes and Heston Models with Stochastic Interest Rates and Term Structure of Volatilities
Alberto Bueno-Guerrero
The Journal of Derivatives Aug 2019, jod.2019.1.078; DOI: 10.3905/jod.2019.1.078

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Black-Scholes and Heston Models with Stochastic Interest Rates and Term Structure of Volatilities
Alberto Bueno-Guerrero
The Journal of Derivatives Aug 2019, jod.2019.1.078; DOI: 10.3905/jod.2019.1.078
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  • Article
    • Abstract
    • A BRIEF REVIEW OF THE CLASSICAL MODELS
    • THE GENERALIZED BLACK-SCHOLES MODEL
    • THE GENERALIZED HESTON MODEL
    • CONCLUSIONS
    • ADDITIONAL READING
    • ACKNOWLEDGMENTS
    • APPENDIX
    • ENDNOTES
    • REFERENCES
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