THE VALUE OF AN OPTION TO EXCHANGE ONE ASSET FOR ANOTHER WILLIAM MARGRABE* I. INTRODUCTION SOME COMMON FINANCIAL ARRANGEMENTS are equivalent to options to exchange one risky asset for another: the investment adviser's performance incentive fee, the general margin account, the exchange offer, and the standby commitment. Yet the literature does not discuss the theory of such an option.' In this paper, I develop an equation for the value of the option to exchange one risky asset for another. My theory grows out of the brilliant Black-Scholes (1973) solution to the longstanding call option pricing problem-which assumes that the price of a riskless discount bond grew exponentially at the riskless interest rate-and Merton's (1973) extension-in which the discount bond's value is stochastic until maturity. In section II, I develop the pricing equation for a European-type option to exchange one asset for another. In section III, I show that such an option is worth more alive than dead, which implies that its owner will not exercise it until the last possible moment. Thus, the formula for the European option is also valid for its American counterpart. Since such an option is not only a call, but also a put,
The Journal of Finance – Wiley
Published: Mar 1, 1978
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