The Valuation of Multivariate Contingent Claims in Discrete Time Models




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    • Manchester Business School and New York University, respectively. We thank George Constantinides, Kose John, Patricia Smith, and especially David Nachman for helpful comments on an earlier draft of this paper. Subsequent to the writing of the second draft of this paper, we came across Stulz [26] and Sercu [21] who address a problem similar to that analyzed here.


There are several examples in the literature of contingent claims whose payoffs depend on the outcomes of two or more stochastic variables. Familiar cases of such claims include options on a portfolio of options, options whose exercise price is stochastic, and options to exchange one asset for another. This paper derives risk neutral valuation relationships (RNVRs) in a discrete time setting that facilitate the pricing of such complex contingent claims in two specific cases: joint lognormally distributed underlying variables and constant proportional risk aversion on the part of investors, and joint normally distributed underlying variables and constant absolute risk aversion preferences, respectively. This methodology is then applied to the valuation of several interesting complex contingent claims such as multiperiod bonds, multicurrency option bonds, and investment options.