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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2451/26894
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| Title: | 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. |
| URI: | http://hdl.handle.net/2451/26894 |
| Appears in Collections: | Finance Working Papers
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