Annals of Finance

, Volume 8, Issue 4, pp 507–531 | Cite as

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

Research Article

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, Y2, 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 Y2 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, Y2, and the interest rate. With ambiguity, the equilibrium price of uncertainty associated with Y2 and the equilibrium interest rate can increase or decrease, depending on: (i) the correlations between the shocks in Y2 and those in the output rate and in the other state variable; (ii) the diffusion functions of the stochastic processes for Y2 and for the output rate; and (iii) the gradient of the value function with respect to Y2. 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.

Keywords

Ambiguity Asset pricing Equilibrium price of uncertainty Robust optimization 

JEL Classification

C68 D81 G13 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Facultade de Ciencias Económicas e EmpresariaisRGEA, Universidad de VigoVigoSpain
  2. 2.CEF.UP and Faculdade de EconomiaUniversidade do PortoPortoPortugal

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