An Alternative Valuation Model for Contingent Claims

Abstract

The fundamental valuation equation of Cox, Ingersoll and Ross was expressed in terms of the indirect utility of wealth function. As closed-form solution for the indirect utility is generally unobtainable when investment opportunities are stochastic, existing contingent claims models involving general stochastic processes were almost all derived under the restrictive log utility assumption. An alternative valuation equation is proposed here that depends only on the direct utility function. This alternative valuation approach is applied to derive closed-form solutions for bonds, bond options, individual stocks, and stock options under both power utility and exponential utility functions. Allowable processes for aggregate output, firms' dividends, and state variables are quite general and empirically plausible. The resulting interest rate and stock price dynamics have many empirically plausible properties. Our bond and stock option pricing models with stochastic volatility and stochastic interest rates have most existing models nested. The stock option pricing model is also shown to have the ability to reconcile certain puzzling empirical regularities such as the volatility smile.