Multifrequency jump-diffusions: An equilibrium approach

L. E. CALVET, A. Fisher

Journal of Mathematical Economics

January 2008, vol. 44, n°2, pp.207-226

Departments: Finance

Keywords: Endogenous jumps, General equilibrium, Markov regime-switching, Multifrequency, Fat tails, Stochastic volatility, Time deformation, Volatility component

This paper develops an equilibrium asset pricing economy in which the stock price follows a diffusion with endogenous jumps at multiple frequencies. The consumption and dividend processes are continuous, but regimeshifts in their drifts and volatilities lead to discrete price changes. The size of a jump is endogenous and increases with the persistence of the Markov switch that triggers i1. The dividend specification builds on the parsimonious Markov-switching multifrequency model of Calvet and Fisher (2001). The resulting jump-diffusion price process is therefore specified by a small number of parameters, which remains independent of the state space size. When the number of frequencies goes to infinity, the equilibrium price process converges to a multifractal jump-diffusion