TY - JOUR

T1 - The price of risk and ambiguity in an intertemporal general equilibrium model of asset prices

AU - Faria, Gonçalo

AU - Correia-da-Silva, João

PY - 2012/11

Y1 - 2012/11

N2 - 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.

AB - 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.

KW - Ambiguity

KW - Asset pricing

KW - Equilibrium price of uncertainty

KW - Robust optimization

UR - http://www.scopus.com/inward/record.url?scp=84869877890&partnerID=8YFLogxK

U2 - 10.1007/s10436-012-0197-y

DO - 10.1007/s10436-012-0197-y

M3 - Article

AN - SCOPUS:84869877890

SN - 1614-2446

VL - 8

SP - 507

EP - 531

JO - Annals of Finance

JF - Annals of Finance

IS - 4

ER -