An alternative valuation model for contingent claims

Abstract

This paper studies contingent claim valuation in a Lucas-type exchange economy. The derived fundamental valuation equation differs from its Cox-Ingersoll-Ross production-economy counterpart in that it is expressed in terms of the direct utility function and an exogenous output process, thus offering superior tractability. We apply our approach to derive closed-form solutions for bond, bond option, individual stock, and stock option prices, under a more general setting than allowable in the Cox Ingersoll-Ross framework. The resulting interest rate and stock price dynamics are empirically plausible. Moreover, our stock option pricing formula with stochastic volatility and interest rates can reconcile certain puzzling empirical regularities, including the volatility smile.