Multifrequency jump-diffusions: An equilibrium approach
Abstract
This paper proposes that equilibrium valuation is a powerful method to generate endogenous jumps in asset prices. We specify an economy with continuous consumption and dividend paths, in which endogenous price jumps originate from the market impact of regime-switches in the drifts and volatilities of fundamentals. We parsimoniously incorporate regimes of heterogeneous durations and verify that the persistence of a shock endogenously increases the magnitude of the induced price jump. As the number of frequencies driving fundamentals goes to infinity, the price process converges to a novel stochastic process, which we call a multifractal jump-diffusion.