The Valuation of Options When Asset Returns Are Generated by a Binomial Process

Authors

  • R. C. STAPLETON,

  • M. G. SUBRAHMANYAM

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    • Manchester Business School, England, and New York University, respectively. We thank K. John for helpful discussion.

ABSTRACT

This paper values options on assets whose returns, over a finite interval of time, are generated by a binomial process. It shows that a simple valuation relationship, between the option and the underlying stock, obtains if investors have preference functions that belong to a particular class, even if opportunities to hedge do not exist. One particular application of the theory is in the case where the stock price over a finite interval could increase by an amount, fall by the same amount, or stay at the same level. The results in this paper may be viewed as the foundation of the preference-based approaches to obtaining a risk neutral valuation relationship.

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