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Option Pricing in a Multi-Asset, Complete Market Economy

Published online by Cambridge University Press:  06 April 2009

Ren-Raw Chen ,
San-Lin Chung  and
Tyler T. Yang
Ren-Raw Chen
Affiliation:
[email protected], Rutgers Business School, Rutgers University, 94 Rockafeller Road, Piscataway, NJ 08854
San-Lin Chung
Affiliation:
[email protected], Department of Finance, National Central University, Taiwan, R.O.C.
Tyler T. Yang
Affiliation:
[email protected], IFE Group, 51 Monroe Street, Plaza E6, Rockville, MD 20850.
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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.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 37 , Issue 4 , December 2002 , pp. 649 - 666
Copyright
Copyright © School of Business Administration, University of Washington 2002

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