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Bounding the values of financial derivatives by the use of the moment problem

Author

Listed:
  • Mariya Naumova

    (Rutgers The State University of New Jersey)

  • András Prékopa

    (Rutgers The State University of New Jersey)

Abstract

Lower and upper bounds are derived on single-period European options under moment information, without assuming that the asset prices follow geometric Brownian motion, which is frequently untrue in practice. Sometimes the entire asset distribution is not completely known, sometimes it is known but the numerical calculation is easier by the use of the moments than the entire probability distribution. As geometric Brownian motion assumption regarding the asset prices is frequently untrue in practice. Some of the bounds are given by formulas, some are obtained by solving special linear programming problems. The bounds can be made close if a sufficiently large number of moments is used, and may serve for approximation of the values of financial derivatives.

Suggested Citation

  • Mariya Naumova & András Prékopa, 2021. "Bounding the values of financial derivatives by the use of the moment problem," Annals of Operations Research, Springer, vol. 305(1), pages 211-225, October.
    • Handle: RePEc:spr:annopr:v:305:y:2021:i:1:d:10.1007_s10479-020-03839-7
    DOI: 10.1007/s10479-020-03839-7
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    References listed on IDEAS

    as
    1. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
    4. repec:bla:jfinan:v:43:y:1988:i:2:p:301-08 is not listed on IDEAS
    5. 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.
    6. Ritchken, Peter H, 1985. "On Option Pricing Bounds," Journal of Finance, American Finance Association, vol. 40(4), pages 1219-1233, September.
    7. Lo, Andrew W., 1987. "Semi-parametric upper bounds for option prices and expected payoffs," Journal of Financial Economics, Elsevier, vol. 19(2), pages 373-387, December.
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