The price of risk and ambiguity in an intertemporal general equilibrium model of asset prices

Abstract

We consider a version of the intertemporal general equilibrium model of Cox et al. (Econometrica 53:363-384, 1985) with a single production process and two correlated state variables. It is assumed that only one of them, Y 2, has shocks correlated with those of the economy's output rate and, simultaneously, that the representative agent is ambiguous about its stochastic process. This implies that changes in Y 2 should be hedged and its uncertainty priced, with this price containing risk and ambiguity components. Ambiguity impacts asset pricing through two channels: the price of uncertainty associated with the ambiguous state variable, Y 2, and the interest rate. With ambiguity, the equilibrium price of uncertainty associated with Y 2 and the equilibrium interest rate can increase or decrease, depending on: (i) the correlations between the shocks in Y 2 and those in the output rate and in the other state variable; (ii) the diffusion functions of the stochastic processes for Y 2 and for the output rate; and (iii) the gradient of the value function with respect to Y 2. As applications of our generic setting, we deduct the model of Longstaff and Schwartz (J Financ 47:1259-1282, 1992) for interest-rate-sensitive contingent claim pricing and the variance-risk price specification in the option pricing model of Heston (Rev Financ Stud 6:327-343, 1993). Additionally, it is obtained a variance-uncertainty price specification that can be used to obtain a closed-form solution for option pricing with ambiguity about stochastic variance. Â(c) 2012 Springer-Verlag.