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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.

Suggested Citation

  • Andrea Gamba & Lenos Trigeorgis, 2007. "An Improved Binomial Lattice Method for Multi-Dimensional Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 453-475.
    • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:5:p:453-475
    DOI: 10.1080/13504860701532237
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    2. Gastón Silverio Milanesi, 2022. "Opciones reales secuenciales cuadrinomiales y volatilidad cambiante: incertidumbres tecnológicas," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 17(1), pages 1-26, Enero - M.
    3. Xuemei Gao & Dongya Deng & Yue Shan, 2014. "Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-6, April.
    4. Carlos Andres Zapata Quimbayo & Carlos Armando Mej¨ªa Vega, 2019. "Real Options Valuation in Gold Mining Projects under Multinomial Tree Approach," Business and Economic Research, Macrothink Institute, vol. 9(3), pages 204-218, September.
    5. Kyoung-Sook Moon & Hongjoong Kim, 2013. "A multi-dimensional local average lattice method for multi-asset models," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 873-884, May.
    6. 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).
    7. Andrea Gamba & Nicola Fusari, 2009. "Valuing Modularity as a Real Option," Management Science, INFORMS, vol. 55(11), pages 1877-1896, November.
    8. Carlos Andrés Zapata Quimbayo, 2020. "OPCIONES REALES Una guía teórico-práctica para la valoración de inversiones bajo incertidumbre mediante modelos en tiempo discreto y simulación de Monte Carlo," Books, Universidad Externado de Colombia, Facultad de Finanzas, Gobierno y Relaciones Internacionales, number 138, April.
    9. 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).
    10. Jarno Talponen & Minna Turunen, 2022. "Option pricing: a yet simpler approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 57-81, June.
    11. Dirk Sierag & Bernard Hanzon, 2018. "Pricing derivatives on multiple assets: recombining multinomial trees based on Pascal’s simplex," Annals of Operations Research, Springer, vol. 266(1), pages 101-127, July.
    12. Jarno Talponen & Minna Turunen, 2017. "Option pricing: A yet simpler approach," Papers 1705.00212, arXiv.org, revised Mar 2018.
    13. Laude, Audrey & Jonen, Christian, 2013. "Biomass and CCS: The influence of technical change," Energy Policy, Elsevier, vol. 60(C), pages 916-924.
    14. Milanesi, Gastón Silverio, 2023. "Valoración de estrategias competitivas, acuerdos colaborativos y penalizaciones con Opciones Reales Multinomiales y Teoría de Juegos [Valuation of competitive strategies, collaborative agreements a," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 35(1), pages 360-388, June.

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    More about this item

    Keywords

    Option pricing; binomial lattice; multi-dimensional diffusion; JEL classification : G13;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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