Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1

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  • 1

    This paper includes the content from earlier papers by K. Amin, “Pricing American Options in a Term Structure Economy,” 1989, and R. Jarrow, “Option Valuation of Risky Assets in a Stochastic Interest Rate Economy,” 1988. Helpful comments from Robin Brenner, Peter Carr, David Heath, and the participants of the Finance Workshop at Cornell University are gratefully acknowledged.

Abstract

This paper studies contingent claim valuation of risky assets in a stochastic interest rate economy. the model employed generalizes the approach utilized by Heath, Jarrow, and Morton (1992) by imbedding their stochastic interest rate economy into one containing an arbitrary number of additional risky assets. We derive closed form formulae for certain types of European options in this context, notably call and put options on risky assets, forward contracts, and futures contracts. We also value American contingent claims whose payoffs are permitted to be general functions of both the term structure and asset prices generalizing Bensoussan (1984) and Karatzas (1988) in this regard. Here, we provide an example where an American call's value is well defined, yet there does not exist an optimal trading strategy which attains this value. Furthermore, this example is not pathological as it is a generalization of Roll's (1977) formula for a call option on a stock that pays discrete dividends.

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