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American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations

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  • Svetlana Boyarchenko
  • Sergei LevendorskiĬ

Abstract

We consider the Heston model with the stochastic interest rate of Cox--Ingersoll--Ross (CIR) type and more general models with stochastic volatility and interest rates depending on two CIR-factors; the price, volatility and interest rate may correlate. Time-derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options arising in the time discretization of a Markov-modulated L�vy model. Options in this sequence are solved using an iteration method based on the Wiener--Hopf factorization. Typical shapes of the early exercise boundary are shown, and good agreement of option prices with prices calculated with the Longstaff--Schwartz method and Medvedev--Scaillet asymptotic method is demonstrated.

Suggested Citation

  • Svetlana Boyarchenko & Sergei LevendorskiĬ, 2013. "American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(1), pages 26-49, March.
    • Handle: RePEc:taf:apmtfi:v:20:y:2013:i:1:p:26-49
    DOI: 10.1080/1350486X.2012.655935
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    Citations

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    Cited by:

    1. O. Samimi & Z. Mardani & S. Sharafpour & F. Mehrdoust, 2017. "LSM Algorithm for Pricing American Option Under Heston–Hull–White’s Stochastic Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 173-187, August.
    2. Sergei Levendorskiĭ, 2022. "Operators and Boundary Problems in Finance, Economics and Insurance: Peculiarities, Efficient Methods and Outstanding Problems," Mathematics, MDPI, vol. 10(7), pages 1-36, March.
    3. Andrey Itkin, 2015. "LSV models with stochastic interest rates and correlated jumps," Papers 1511.01460, arXiv.org, revised Nov 2016.
    4. L. C. G. Rogers, 2015. "Bermudan options by simulation," Papers 1508.06117, arXiv.org, revised Jan 2016.
    5. Anna Battauz & Francesco Rotondi, 2022. "American options and stochastic interest rates," Computational Management Science, Springer, vol. 19(4), pages 567-604, October.
    6. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "Efficient evaluation of double-barrier options and joint cpdf of a L\'evy process and its two extrema," Papers 2211.07765, arXiv.org.
    7. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.

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