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On the Evaluation of Compound Options

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Author Info

  • 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)

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    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.33.3.347
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 33 (1987)
    Issue (Month): 3 (March)
    Pages: 347-355

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    Handle: RePEc:inm:ormnsc:v:33:y:1987:i:3:p:347-355

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    Related research

    Keywords: American call; American put; computational efficiency; contingent claims; coupon bonds; identity; multinormal; nested;

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    Cited by:
    1. Stylianos PERRAKIS & Jean LEFOLL, 1999. "Option Pricing and Replication with Transaction Costs and Dividends," FAME Research Paper Series rp8, International Center for Financial Asset Management and Engineering.
    2. 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.
    3. Marti G. Subrahmanyam & Bin Gao & Jing-zhi Huang, 1998. "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-067, New York University, Leonard N. Stern School of Business-.
    4. Mark Broadie & Jérôme B. Detemple & Eric Ghysels & Olivier Torrès, 1996. "Nonparametric Estimation of American Options Exercise Boundaries and Call Prices," CIRANO Working Papers 96s-24, CIRANO.
    5. 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.

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