Consistency of (Intertemporal) Beta Asset Pricing and Black-Scholes Option Valuation

Abstract

It is well-known that the CAPM valuation formula results from a quadratic utility of the representative investor. In this paper we show that the CAPM valuation rule remains valid if the representative investor exhibits an exponential utility and asset and market returns are bivariate normally distributed. In contrast to quadratic utility, exponential utility implies a positive stochastic discount factor that guarantees positive (option) prices. In particular, within our discrete-time framework, options are priced according to the Black-Scholes formula. In addition, our approach allows the valuation of single assets if their return follows an intertemporal market model with stochastic beta. The resulting valuation formula differs from the standard CAPM only in that the expected beta replaces the deterministic one. It turns out that the expected beta can easily be estimated from the return time series.