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The closed-form approximation to price basket options under stochastic interest rate

Author

Listed:
  • Yu, Bo
  • Zhu, Hongmei
  • Wu, Ping

Abstract

The paper presents closed-form approximation formulas for pricing basket options. We assume that the underlying asset prices follow geometric Brownian motions and the interest rate follows the one-factor Hull-White model. Under a given forward measure, we obtain the analytical lower and upper bounds of basket options. By finding a simple random variable to replace the sum of the lognormal random variables, we combine the conditioning and the moment matching approaches, and derive approximation formulas to price basket options. Numerical results illustrate that our results fall in the sharp lower and upper bounds of basket options and are consistent with Monte Carlo simulation results.

Suggested Citation

  • Yu, Bo & Zhu, Hongmei & Wu, Ping, 2022. "The closed-form approximation to price basket options under stochastic interest rate," Finance Research Letters, Elsevier, vol. 46(PB).
    • Handle: RePEc:eee:finlet:v:46:y:2022:i:pb:s1544612321004232
    DOI: 10.1016/j.frl.2021.102434
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    References listed on IDEAS

    as
    1. Ping Wu & Robert J. Elliott, 2017. "A simple efficient approximation to price basket stock options with volatility smile," Annals of Finance, Springer, vol. 13(1), pages 1-29, February.
    2. Deelstra, G. & Liinev, J. & Vanmaele, M., 2004. "Pricing of arithmetic basket options by conditioning," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 55-77, February.
    3. Ruggero Caldana & Gianluca Fusai & Alessandro Gnoatto & Martino Grasselli, 2016. "General closed-form basket option pricing bounds," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 535-554, April.
    4. Griselda Deelstra & Jan Liinev & Michèle Vanmaele, 2004. "Pricing of arithmetic basket options by conditioning," ULB Institutional Repository 2013/7600, ULB -- Universite Libre de Bruxelles.
    5. Moshe Arye Milevsky & Steven E. Posner, 1999. "Asian Options, The Sum Of Lognormals, And The Reciprocal Gamma Distribution," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 7, pages 203-218, World Scientific Publishing Co. Pte. Ltd..
    6. Dilip Madan, 2010. "Pricing and hedging basket options to prespecified levels of acceptability," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 607-615.
    7. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Basket options; Forward valuation method; Log-normal distribution; Moment matching approach; Conditioning approach;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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