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An Improved Binomial Lattice Method for Multi-Dimensional Options

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  • Andrea Gamba
  • Lenos Trigeorgis

Abstract

A binomial lattice approach is proposed for valuing options whose payoff depends on multiple state variables following correlated geometric Brownian processes. The proposed approach relies on two simple ideas: a log-transformation of the underlying processes, which is step by step consistent with the continuous-time diffusions, and a change of basis of the asset span, to transform asset prices into uncorrelated processes. An additional transformation is applied to approximate driftless dynamics. Even if these features are simple and straightforward to implement, it is shown that they significantly improve the efficiency of the multi-dimensional binomial algorithm. A thorough test of efficiency is provided compared with most popular binomial and trinomial lattice approaches for multi-dimensional diffusions. Although the order of convergence is the same for all lattice approaches, the proposed method shows improved efficiency.

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File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701532237
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 14 (2007)
Issue (Month): 5 ()
Pages: 453-475

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Handle: RePEc:taf:apmtfi:v:14:y:2007:i:5:p:453-475

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Related research

Keywords: Option pricing; binomial lattice; multi-dimensional diffusion; JEL classification : G13;

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References

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  1. Chen, Ren-Raw & Chung, San-Lin & Yang, Tyler T., 2002. "Option Pricing in a Multi-Asset, Complete Market Economy," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(04), pages 649-666, December.
  2. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
  3. Constantinides, George M, 1978. "Market Risk Adjustment in Project Valuation," Journal of Finance, American Finance Association, vol. 33(2), pages 603-16, May.
  4. Amin, Kaushik I., 1991. "On the Computation of Continuous Time Option Prices Using Discrete Approximations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(04), pages 477-495, December.
  5. 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.
  6. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-50.
  7. Gonzalo Cortazar & Eduardo S. Schwartz & Marcelo Salinas, 1998. "Evaluating Environmental Investments: A Real Options Approach," Management Science, INFORMS, vol. 44(8), pages 1059-1070, August.
  8. Ekvall, Niklas, 1996. "A lattice approach for pricing of multivariate contingent claims," European Journal of Operational Research, Elsevier, vol. 91(2), pages 214-228, June.
  9. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-62, May.
  10. Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(02), pages 153-164, June.
  11. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March.
  12. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
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Citations

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Cited by:
  1. Andrea Gamba & Nicola Fusari, 2009. "Valuing Modularity as a Real Option," Management Science, INFORMS, vol. 55(11), pages 1877-1896, November.
  2. Rohlfs, Wilko & Madlener, Reinhard, 2011. "Multi-Commodity Real Options Analysis of Power Plant Investments: Discounting Endogenous Risk Structures," FCN Working Papers 22/2011, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
  3. Laude, Audrey & Jonen, Christian, 2013. "Biomass and CCS: The influence of technical change," Energy Policy, Elsevier, vol. 60(C), pages 916-924.
  4. Rohlfs, Wilko & Madlener, Reinhard, 2013. "Optimal Power Generation Investment: Impact of Technology Choices and Existing Portfolios for Deploying Low-Carbon Coal Technologies," FCN Working Papers 12/2013, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).

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