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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. Weinan Zhang & Pingping Zeng, 2023. "A transform-based method for pricing Asian options under general two-dimensional models," Quantitative Finance, Taylor & Francis Journals, vol. 23(11), pages 1677-1697, November.
    5. L. C. G. Rogers, 2015. "Bermudan options by simulation," Papers 1508.06117, arXiv.org, revised Jan 2016.
    6. Anna Battauz & Francesco Rotondi, 2022. "American options and stochastic interest rates," Computational Management Science, Springer, vol. 19(4), pages 567-604, October.
    7. 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.
    8. 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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