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New Splitting Scheme for Pricing American Options Under the Heston Model

Author

Listed:
  • Maryam Safaei

    (Islamic Azad University)

  • Abodolsadeh Neisy

    (Allameh Tabataba’i University)

  • Nader Nematollahi

    (Allameh Tabataba’i University)

Abstract

In this paper, we present a new splitting scheme for pricing the American options under the Heston model. For this purpose, first the price of American put option is modeled, which its underlying asset value follows Heston’s stochastic volatility model , and then it is formulated as a linear complementarity problem (LCP) involving partial differential operator. By using new splitting scheme, the partial differential operator is decomposed into simpler operators in several fractional time steps. These operators are implicitly expressed in the implicit Adams–Moulton method. Then, the two-dimensional LCP is decomposed into three LCPs based on these operators. Each LCP is solved numerically in two steps. The numerical results obtained for the American option pricing problem based on the Heston model are compared with the reference results.

Suggested Citation

  • Maryam Safaei & Abodolsadeh Neisy & Nader Nematollahi, 2018. "New Splitting Scheme for Pricing American Options Under the Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 405-420, August.
    • Handle: RePEc:kap:compec:v:52:y:2018:i:2:d:10.1007_s10614-017-9686-4
    DOI: 10.1007/s10614-017-9686-4
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    3. Tinne Haentjens & Karel J. in 't Hout, 2015. "ADI Schemes for Pricing American Options under the Heston Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 207-237, July.
    4. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(4), pages 589-607, December.
    5. 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.
    6. 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.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Cited by:

    1. Y. Esmaeelzade Aghdam & A. Neisy & A. Adl, 2024. "Simulating and Pricing CAT Bonds Using the Spectral Method Based on Chebyshev Basis," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 423-435, January.
    2. Kozpınar, Sinem & Uzunca, Murat & Karasözen, Bülent, 2020. "Pricing European and American options under Heston model using discontinuous Galerkin finite elements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 568-587.

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