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

*Gonçalo Faria* () and
*Joao Correia-da-Silva*

*Annals of Finance*, 2012, vol. 8, issue 4, 507-531

**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. Copyright Springer-Verlag 2012

**Keywords:** Ambiguity; Asset pricing; Equilibrium price of uncertainty; Robust optimization; C68; D81; G13 (search for similar items in EconPapers)

**Date:** 2012

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**Citations:** View citations in EconPapers (8)

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Working Paper: The Price of Risk and Ambiguity in an Intertemporal General Equilibrium Model of Asset Prices (2011)

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**Persistent link:** https://EconPapers.repec.org/RePEc:kap:annfin:v:8:y:2012:i:4:p:507-531

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**DOI:** 10.1007/s10436-012-0197-y

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