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

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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.

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Authors and Affiliations

  1. Facultade de Ciencias Económicas e Empresariais, RGEA, Universidad de Vigo, Lagoas Marcosende, 36310, Vigo, Spain

    Gonçalo Faria

  2. CEF.UP and Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-464, Porto, Portugal

    João Correia-da-Silva

Authors
  1. Gonçalo Faria
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  2. João Correia-da-Silva
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Correspondence to Gonçalo Faria.

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Faria, G., Correia-da-Silva, J. The price of risk and ambiguity in an intertemporal general equilibrium model of asset prices. Ann Finance 8, 507–531 (2012). https://doi.org/10.1007/s10436-012-0197-y

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  • DOI: https://doi.org/10.1007/s10436-012-0197-y

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