Pricing of the Time-Change Risks
41 Pages Posted: 1 Aug 2008 Last revised: 13 Dec 2011
Date Written: April 1, 2008
We develop a discrete-time real endowment economy featuring Epstein-Zin recursive utility and a Levy time-change subordinator, which represents a clock that connects business time to calendar time. This setup provides a convenient equilibrium framework for pricing non-Gaussian risks, where the solutions for financial prices are available up to integral operations in general, or in closed-form for tempered stable shocks. The non-Gaussianity of fundamentals due to time-deformation induces compensations for higher order moments and co-moments of consumption and dividend growth rates of the assets. Forecastability of the time change leads to predictability of the endowment streams and therefore to time-variation in financial prices and risk premia on assets. In numerical calibrations, we quantitatively analyze the compensations for different types of systematic risk.
Keywords: Risk premium, time change, Levy processes, recursive preferences
JEL Classification: G12, D51, C51
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