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Pricing American options under stochastic volatility and stochastic interest rates

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  • Medvedev, Alexey
  • Scaillet, Olivier

Abstract

We introduce a new analytical approach to price American options. Using an explicit and intuitive proxy for the exercise rule, we derive tractable pricing formulas using a short-maturity asymptotic expansion. Depending on model parameters, this method can accurately price options with time-to-maturity up to several years. The main advantage of our approach over existing methods lies in its straightforward extension to models with stochastic volatility and stochastic interest rates. We exploit this advantage by providing an analysis of the impact of volatility mean-reversion, volatility of volatility, and correlations on the American put price.

Suggested Citation

  • Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
  • Handle: RePEc:eee:jfinec:v:98:y:2010:i:1:p:145-159
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Beliaeva, Natalia & Nawalkha, Sanjay, 2012. "Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 151-163.
    2. Gong, Pu & Dai, Jun, 2017. "Pricing real estate index options under stochastic interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 309-323.
    3. repec:eee:dyncon:v:80:y:2017:i:c:p:75-100 is not listed on IDEAS
    4. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, "undated". "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    5. Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," Working Papers - Mathematical Economics 2012-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    6. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    7. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & Olivier Scaillet, 2016. "Early exercise decision in American options with dividends, stochastic volatility and jumps," Papers 1612.03031, arXiv.org.
    8. Andrey Itkin, 2015. "LSV models with stochastic interest rates and correlated jumps," Papers 1511.01460, arXiv.org, revised Nov 2016.
    9. Jin, Xing & Li, Xun & Tan, Hwee Huat & Wu, Zhenyu, 2013. "A computationally efficient state-space partitioning approach to pricing high-dimensional American options via dimension reduction," European Journal of Operational Research, Elsevier, vol. 231(2), pages 362-370.
    10. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, pages 177-217.
    11. Anna Battauz & Marzia De Donno & Alessandro Sbuelz, 2015. "Real Options and American Derivatives: The Double Continuation Region," Management Science, INFORMS, vol. 61(5), pages 1094-1107, May.
    12. L. C. G. Rogers, 2015. "Bermudan options by simulation," Papers 1508.06117, arXiv.org, revised Jan 2016.

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