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Option Pricing in a Multi-Asset, Complete Market Economy

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  • Chen, Ren-Raw
  • Chung, San-Lin
  • Yang, Tyler T.

Abstract

This paper extends the seminal Cox-Ross-Rubinstein ((1979), CRR hereafter) binomial model to multiple assets. It differs from previous models in that it is derived under the complete market environment specified by Duffie and Huang (1985) and He (1990). The complete market assumption requires the number of states to grow linearly with the number of assets. However, the number of correlations grows at a faster rate, causing the CRR model to be indirectly extendable. We solve such a problem by recognizing that the fast growing correlation number is matched by the number of the angles of the edges of a hypercube spanned by the risky assets. As a result, we derive a solution that allows the number of equations to equal the number of risky assets and the riskless bond. The resulting tree structure hence provides the same intuition of pricing and hedging contingent claims as that provided by the CRR model. Finally, the proposed model is not only as easy to implement as the one-dimensional CRR model but also it is more memory efficient than the existing multi-factor lattice models.

Suggested Citation

  • 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(4), pages 649-666, December.
    • Handle: RePEc:cup:jfinqa:v:37:y:2002:i:04:p:649-666_00
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    Cited by:

    1. Arkadiy V. Sakhartov & Timothy B. Folta, 2014. "Resource relatedness, redeployability, and firm value," Strategic Management Journal, Wiley Blackwell, vol. 35(12), pages 1781-1797, December.
    2. 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.
    3. 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.
    4. Christian Gourieroux & Razvan Sufana, 2004. "Derivative Pricing with Multivariate Stochastic Volatility : Application to Credit Risk," Working Papers 2004-31, Center for Research in Economics and Statistics.
    5. Peter W. Duck & Chao Yang & David P. Newton & Martin Widdicks, 2009. "Singular Perturbation Techniques Applied To Multiasset Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 457-486, July.
    6. 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.
    7. Ren-Raw Chen & Jeffrey Huang & William Huang & Robert Yu, 2021. "An Artificial Intelligence Approach to the Valuation of American-Style Derivatives: A Use of Particle Swarm Optimization," JRFM, MDPI, vol. 14(2), pages 1-22, February.
    8. Jing Li & Charles Dhanaraj & Richard L. Shockley, 2008. "Joint venture evolution: extending the real options approach," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 29(4), pages 317-336.

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