Skip navigation

Forecasting Multifractal Volatility

Authors: Calvet, Laurent
Fisher, Adlai
Keywords: Forecasting;Implied Volatility;Long Memory;Multifractal Model of Asset Returns;Option Pricing;Poisson Multifractal;Trading Time;Volatility Smile
Issue Date: Feb-1999
Series/Report no.: FIN-99-017
Abstract: 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.
Appears in Collections:Finance Working Papers

Files in This Item:
File Description SizeFormat 
wpa99017.pdf1.37 MBAdobe PDFView/Open

Items in FDA are protected by copyright, with all rights reserved, unless otherwise indicated.