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On the Evaluation of Compound Options

Author

Listed:
  • Michael J. P. Selby

    (Morgan Grenfell Securities Holdings Ltd., P.O. Box 479, 20 Finsbury Circus, London, EC2M 7BB, United Kingdom)

  • Stewart D. Hodges

    (School of Industrial and Business Studies, Warwick University, Warwick, United Kingdom)

Abstract

Compound option valuation formulae give rise to the summation of a series of multinormal distribution functions. This paper presents an identity on sums of nested multinormal distributions of arbitrary dimension. We show that this identity generalizes some well-known low order identities for the multinormal distribution. We present three applications of the new identity to contingent claims valuation problems. The first and second applications show that by reducing significantly the number of integrals to be evaluated, faster and more accurate algorithms can be developed for implementing the Geske-Johnson American put valuation formula and the Roll-Geske-Whaley American call formula; the third gives new economic insights into the valuation of disaggregated coupon bonds.

Suggested Citation

  • Michael J. P. Selby & Stewart D. Hodges, 1987. "On the Evaluation of Compound Options," Management Science, INFORMS, vol. 33(3), pages 347-355, March.
    • Handle: RePEc:inm:ormnsc:v:33:y:1987:i:3:p:347-355
    DOI: 10.1287/mnsc.33.3.347
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    Citations

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    Cited by:

    1. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
    2. Gukhal, C.R.Chandrasekhar Reddy, 2004. "The compound option approach to American options on jump-diffusions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2055-2074, September.
    3. L. Sereno, 2006. "The Valuation of New Ventures," Working Papers 554, Dipartimento Scienze Economiche, Universita' di Bologna.
    4. B. Gao J. Huang, "undated". "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-002, New York University, Leonard N. Stern School of Business-.
    5. Yepes Rodri­guez, Ramón, 2008. "Real option valuation of free destination in long-term liquefied natural gas supplies," Energy Economics, Elsevier, vol. 30(4), pages 1909-1932, July.
    6. Rossella Agliardi, 2011. "A comprehensive structural model for defaultable fixed-income bonds," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 749-762.
    7. Pierangelo Ciurlia & Ilir Roko, 2005. "Valuation of American Continuous-Installment Options," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 143-165, February.
    8. Roland Mallier & Ghada Alobaidi, 2000. "Laplace transforms and American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(4), pages 241-256.
    9. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    10. Gao, Bin & Huang, Jing-zhi & Subrahmanyam, Marti, 2000. "The valuation of American barrier options using the decomposition technique," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1783-1827, October.
    11. Xing Gao & Daniel Ladley, 2022. "Noise trading and market stability," The European Journal of Finance, Taylor & Francis Journals, vol. 28(13-15), pages 1283-1301, October.
    12. Pavel V. Gapeev, 2022. "Perpetual American Double Lookback Options on Drawdowns and Drawups with Floating Strikes," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 749-788, June.
    13. Perrakis, Stylianos & Lefoll, Jean, 2000. "Option pricing and replication with transaction costs and dividends," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1527-1561, October.
    14. Axel Pierru & Alessandro Mauro, 1999. "Actions et obligations : des options qui s'ignorent," Working Papers hal-02437338, HAL.
    15. P. L. Varson & M. J. P. Selby, 1997. "Option prices as predictors of stock prices: intraday adjustments to information releases," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 49-72, March.
    16. L. Sereno, 2006. "Valuing R & D Investments With A Jump-Diffusion Process," Working Papers 569, Dipartimento Scienze Economiche, Universita' di Bologna.
    17. Dean Paxson, 2007. "Sequential American Exchange Property Options," The Journal of Real Estate Finance and Economics, Springer, vol. 34(1), pages 135-157, January.
    18. Foad Shokrollahi, 2017. "Pricing compound and extendible options under mixed fractional Brownian motion with jumps," Papers 1708.04829, arXiv.org.

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