Multifrequency Jump-Diffusions: An Equilibrium Approach

35 Pages Posted: 20 Dec 2006 Last revised: 7 May 2013

See all articles by Laurent E. Calvet

Laurent E. Calvet

EDHEC Business School - Department of Economics & Finance; CEPR

Adlai J. Fisher

University of British Columbia (UBC) - Sauder School of Business

Multiple version iconThere are 2 versions of this paper

Date Written: January 1, 2008

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.

Keywords: Endogenous jumps, general equilibrium, Markov regime-switching, multifrequency, fat tails, stochastic volatility, time deformation, volatility component

JEL Classification: G0, C5

Suggested Citation

Calvet, Laurent E. and Fisher, Adlai J., Multifrequency Jump-Diffusions: An Equilibrium Approach (January 1, 2008). Journal of Mathematical Economics, Vol. 44, No. 2, 2008. Available at SSRN: https://ssrn.com/abstract=952411 or http://dx.doi.org/10.2139/ssrn.952411

Laurent E. Calvet (Contact Author)

EDHEC Business School - Department of Economics & Finance ( email )

France

CEPR ( email )

33 Great Sutton Street
London, EC1V 0DX
United Kingdom

Adlai J. Fisher

University of British Columbia (UBC) - Sauder School of Business ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada
604-822-8331 (Phone)
604-822-4695 (Fax)

HOME PAGE: http://finance.sauder.ubc.ca/~fisher

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