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ADI schemes for pricing American options under the Heston model

Author

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  • Tinne Haentjens
  • Karel in 't Hout

Abstract

In this paper a simple, effective adaptation of Alternating Direction Implicit (ADI) time discretization schemes is proposed for the numerical pricing of American-style options under the Heston model via a partial differential complementarity problem. The stability and convergence of the new methods are extensively investigated in actual, challenging applications. In addition a relevant theoretical result is proved.

Suggested Citation

  • Tinne Haentjens & Karel in 't Hout, 2013. "ADI schemes for pricing American options under the Heston model," Papers 1309.0110, arXiv.org.
    • Handle: RePEc:arx:papers:1309.0110
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    File URL: http://arxiv.org/pdf/1309.0110
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    References listed on IDEAS

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    1. Samuli Ikonen & Jari Toivanen, 2007. "Componentwise Splitting Methods For Pricing American Options Under Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 331-361.
    2. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    3. Nigel Clarke & Kevin Parrott, 1999. "Multigrid for American option pricing with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 177-195.
    4. Stephane Villeneuve & Antonino Zanette, 2002. "Parabolic ADI Methods for Pricing American Options on Two Stocks," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 121-149, February.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. Cornelis S. L. De Graaf & Qian Feng & Drona Kandhai & Cornelis W. Oosterlee, 2014. "Efficient Computation Of Exposure Profiles For Counterparty Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-23.

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