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A Lattice Framework for Option Pricing with Two State Variables

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Author Info
Boyle, Phelim P.
Abstract

A procedure is developed for the valuation of options when there are two underlying state variables. The approach involves an extension of the lattice binomial approach developed by Cox, Ross, and Rubinstein to value options on a single asset. Details are given on how the jump probabilities and jump amplitudes may be obtained when there are two state variables. This procedure can be used to price any contingent claim whose payoff is a piece-wise linear function of two underlying state variables, provided these two variables have a bivariate lognormal distribution. The accuracy of the method is illustrated by valuing options on the maximum and minimum of two assets and comparing the results for cases in which an exact solution has been obtained for European options. One advantage of the lattice approach is that it handles the early exercise feature of American options. In addition, it should be possible to use this approach to value a number of financial instruments that have been created in recent years.

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Publisher Info
Article provided by Cambridge University Press in its journal Journal of Financial and Quantitative Analysis.

Volume (Year): 23 (1988)
Issue (Month): 01 (March)
Pages: 1-12
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Handle: RePEc:cup:jfinqa:v:23:y:1988:i:01:p:1-12_01

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  1. Collan, Mikael, 2004. "Giga-Investments: Modelling the Valuation of Very Large Industrial Real Investments," MPRA Paper 4328, University Library of Munich, Germany. [Downloadable!]
  2. Joshua Rosenberg, 1999. "Semiparametric Pricing of Multivariate Contingent Claims," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-028, New York University, Leonard N. Stern School of Business-. [Downloadable!]
  3. 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. [Downloadable!]
  4. Yoram Landskroner & Alon Raviv, 2004. "The Valuation of Inflation-Indexed and FX Convertible Bonds," Finance 0401005, EconWPA. [Downloadable!]
  5. Andrea Gam & Paolo Pellizzari, 2002. "Utility based pricing of contingent claims in incomplete markets," Applied Mathematical Finance, Taylor and Francis Journals, vol. 9(4), pages 241-260, December. [Downloadable!] (restricted)
  6. Ilhem Kassar & Pierre Lasserre, 2002. "Species Preservation and Biodiversity Value: A Real Options Approach," CIRANO Working Papers 2002s-82, CIRANO. [Downloadable!]
    Other versions:
  7. Vladislav Kargin, 2003. "Lattice Option Pricing By Multidimensional Interpolation," Finance 0309003, EconWPA, revised 29 Oct 2004. [Downloadable!]
    Other versions:
  8. A. Gamba & P. Pellizzari, 1999. "Utility based pricing of contingent claims," Finance 9902003, EconWPA, revised 14 Oct 2002. [Downloadable!]
  9. Rachel A. Campbell & Roman Kräussl, 2006. "Does Patience Pay? Empirical Testing of the Option to Delay Accepting a Tender Offer in the U.S. Banking Sector," CFS Working Paper Series 2006/32, Center for Financial Studies. [Downloadable!]
  10. Augusto Castillo, 2004. "Firm and Corporate Bond Valuation: A Simulation Dynamic Programming Approach," Cuadernos de Economía (Latin American Journal of Economics), Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 41(124), pages 345-360. [Downloadable!]
  11. Rainer Brosch, 2001. "Portfolio-aspects in real options management," Working Paper Series: Finance and Accounting 66, Department of Finance, Goethe University Frankfurt am Main. [Downloadable!]
  12. Mark Broadie & Jérôme B. Detemple & Eric Ghysels & Olivier Torrès, 1996. "American Options with Stochastic Dividends and Volatility: A Nonparametric Investigation," CIRANO Working Papers 96s-26, CIRANO. [Downloadable!]
    Other versions:
  13. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO. [Downloadable!]
  14. Pizzi Claudio & Pellizzari Paolo, 2002. "Monte Carlo Pricing of American Options Using Nonparametric Regression," Finance 0207007, EconWPA, revised 04 Mar 2003. [Downloadable!]
  15. Massimo Costabile & Arturo Leccadito & Ivar Massabó, 2009. "Computationally simple lattice methods for option and bond pricing," Decisions in Economics and Finance, Springer, vol. 32(2), pages 161-181, November. [Downloadable!] (restricted)
  16. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York. [Downloadable!]
  17. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO. [Downloadable!]
  18. 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. [Downloadable!]
    Other versions:
  19. Mark Rubinstein, 2000. "On the Relation Between Binomial and Trinomial Option Pricing Models," Research Program in Finance, Working Paper Series 1003, Research Program in Finance, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
  20. Manuel Moreno & Javier R. Navas, 2001. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Economics Working Papers 543, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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  21. feng dai, 2004. "The Partial Distribution: Definition, Properties and Applications in Economy," Econometrics 0403008, EconWPA. [Downloadable!]
  22. Phelim P. Boyle, Yisong (Sam) Tian, 1998. "An explicit finite difference approach to the pricing of barrier options," Applied Mathematical Finance, Taylor and Francis Journals, vol. 5(1), pages 17-43, March. [Downloadable!] (restricted)
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