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Multifrequency Jump-Diffusions: An Equilibrium Approach

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  • Laurent E. Calvet
  • Adlai J. Fisher

Abstract

This paper proposes that equilibrium valuation is a powerful method to generate endogenous jumps in asset prices, which provides a structural alternative to traditional reduced-form specifications with exogenous discontinuities. 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 shocks of heterogeneous durations in consumption and dividends while keeping constant the number of parameters. Equilibrium valuation creates an endogenous relation between a shock's persistence and 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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12797.

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Date of creation: Dec 2006
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Publication status: published as Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
Handle: RePEc:nbr:nberwo:12797

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Cited by:
  1. Lars Peter Hansen & Jaroslav BoroviÄka & Mark Hendricks & Jose A. Scheinkman, 2010. "Risk Price Dynamics," Working Papers, Becker Friedman Institute for Research In Economics 2010-004, Becker Friedman Institute for Research In Economics.
  2. Hervé Crès & Tobias Markeprand & Mich Tvede, 2009. "Incomplete Financial Markets and Jumps in Asset Prices," Discussion Papers 09-12, University of Copenhagen. Department of Economics.
  3. Guidolin, Massimo & Timmermann, Allan, 2007. "Asset allocation under multivariate regime switching," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 31(11), pages 3503-3544, November.

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