EQUILIBRIUM STATE PRICES IN A STOCHASTIC VOLATILITY MODEL1

Huyěn Pham and Nizar Touzi

Mathematical Finance, 1996, vol. 6, issue 2, 215-236

Abstract: In a stochastic volatility model, the no‐free‐lunch assumption does not induce a unique arbitrage price because of market incompleteness. In this paper, we consider a contingent claim on the primitive asset, traded in zero net supply. Given a system of Arrow‐Debreu state prices, we provide necessary and sufficient conditions for consistency with an intertemporal additive equilibrium model that we fully characterize. We show that the risk premia corresponding to the minimal martingale of Föllmer and Schweizer (1991) are consistent with logarithmic preferences, while the Hull and White model (1987) (volatility risk premium independent of the asset price) is consistent with a class of utility functions including constant relative risk aversion (CRRA) ones.

Date: 1996
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