Forecasting Multifractal Volatility

48 Pages Posted: 7 Nov 2008

See all articles by Laurent E. Calvet

Laurent E. Calvet

SKEMA Business School; CEPR

Adlai J. Fisher

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

Date Written: February 1999


This paper develops analytical methods to forecast the distribution of future returns for a new continuous-time process, the Poisson multifractal. Out model captures the thick tails and volatility persistence exhibited by many financial time series. We assume that the forecaster knows the true generating process with certainty, but only observes past returns. The challenge in this environment is long memory and the corresponding infinite dimension of the state space. We show that a discretized version of the model has a finite state space, which allows an analytical solution to the conditioning problem. Further, the discrete model converges to the continuous-time model as time scale goes to zero, so that forecasts are consistent. The methodology is implemented on simulated data calibrated to the Deutschemark/US Dollar exchange rate. Applying these results to option pricing, we find that the model captures both volatility smiles and long-memory in the term structure of implied volatilities.

Keywords: Forecasting, Implied Volatility, Long Memory, Multifractal Model of Asset Returns, Option Pricing, Poisson Multifractal, Trading Time, Volatility Smile

Suggested Citation

Calvet, Laurent E. and Fisher, Adlai J., Forecasting Multifractal Volatility (February 1999). NYU Working Paper No. FIN-99-017, Available at SSRN:

Laurent E. Calvet (Contact Author)

SKEMA Business School ( email )

5 Quai Marcel Dassault
Suresnes, 92150

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
604-822-8331 (Phone)
604-822-4695 (Fax)


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