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Multinomial Approximating Models for Options with k State Variables

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Author Info

  • Bardia Kamrad

    (Faculty of Decision Sciences, School of Business Administration, Georgetown University, Washington, D.C. 20057)

  • Peter Ritchken

    (Department of Operations Research, Weatherhead School of Management, Case Western Reserve University, Cleveland, Ohio 44106)

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    Abstract

    Contingent claims whose values depend on multiple sources of uncertainty arise in many financial contracts and in the analysis of real projects. Unfortunately closed form solutions for these options are rare and numerical methods can be computationally expensive. This article extends the literature on multinomial approximating models. Specifically, new multinomial models are presented that include as special cases existing models. The more general models are shown to be computationally more efficient.

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    File URL: http://dx.doi.org/10.1287/mnsc.37.12.1640
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 37 (1991)
    Issue (Month): 12 (December)
    Pages: 1640-1652

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    Handle: RePEc:inm:ormnsc:v:37:y:1991:i:12:p:1640-1652

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    Related research

    Keywords: contingent claims; option pricing; geometric Wiener processes; multinomial lattice;

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    Cited by:
    1. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    2. Babbs, Simon, 2000. "Binomial valuation of lookback options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1499-1525, October.
    3. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
    4. Hu, Xiangling & Motwani, Jaideep G., 2014. "Minimizing downside risks for global sourcing under price-sensitive stochastic demand, exchange rate uncertainties, and supplier capacity constraints," International Journal of Production Economics, Elsevier, vol. 147(PB), pages 398-409.
    5. Lander, Diane M. & Pinches, George E., 1998. "Challenges to the Practical Implementation of Modeling and Valuing Real Options," The Quarterly Review of Economics and Finance, Elsevier, vol. 38(3, Part 2), pages 537-567.
    6. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    7. Donald J. Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Cowles Foundation Discussion Papers 1518, Cowles Foundation for Research in Economics, Yale University.
    8. Robert H. Keeley & Sanjeev Punjabi & Lassaad Turki, 1996. "Valuation of Early-Stage Ventures: Option Valuation Models vs. Traditional Approaches," Journal of Entrepreneurial Finance, Pepperdine University, Graziadio School of Business and Management, vol. 5(2), pages 115-38 , Summer.
    9. Jérôme Lelong & Antonino Zanette, 2010. "Tree methods," Post-Print hal-00776713, HAL.
    10. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    11. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    12. Ben-Ameur, Hatem & de Frutos, Javier & Fakhfakh, Tarek & Diaby, Vacaba, 2013. "Upper and lower bounds for convex value functions of derivative contracts," Economic Modelling, Elsevier, vol. 34(C), pages 69-75.
    13. Luenberger, David G., 1998. "Products of trees for investment analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1403-1417, August.
    14. Mark Rubinstein., 2000. "On the Relation Between Binomial and Trinomial Option Pricing Models," Research Program in Finance Working Papers RPF-292, University of California at Berkeley.
    15. Dangl, Thomas & Wirl, Franz, 2004. "Investment under uncertainty: calculating the value function when the Bellman equation cannot be solved analytically," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1437-1460, April.
    16. Vladislav Kargin, 2003. "Lattice Option Pricing By Multidimensional Interpolation," Finance 0309003, EconWPA, revised 29 Oct 2004.
    17. Donald Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Yale School of Management Working Papers amz2581, Yale School of Management, revised 01 Jul 2005.
    18. Chuang-Chang Chang & Jun-Biao Lin, 2010. "The valuation of multivariate contingent claims under transformed trinomial approaches," Review of Quantitative Finance and Accounting, Springer, vol. 34(1), pages 23-36, January.
    19. Cassimon, D. & Engelen, P.J. & Thomassen, L. & Van Wouwe, M., 2007. "Closed-form valuation of American call options on stocks paying multiple dividends," Finance Research Letters, Elsevier, vol. 4(1), pages 33-48, March.

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