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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2451/27223
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| Title: | A Multifractal Model of Assets Returns |
| Authors: | Calvet, Laurent
Fisher, Adlai |
| Keywords: | Multifractal Model of Asset Returns
Compound Stochastic Process
Time Deformation
Scaling
Self-Similarity
Multifractal Spectrum
Stochastic Volatility |
| Issue Date: | 10-Nov-1999 |
| Series/Report no.: | FIN-99-072 |
| Abstract: | This paper investigates the Multifractal Model of Asset Returns, a
continuous-time process that incorporates the thick tails and volatility
persistence exhibited by many financial time series. The model is
constructed by compounding a Brownian Motion with a multifractal
time-deformation process. Return moments scale as a power law of the
time horizon, a property confirmed for Deutschemark / U.S. Dollar
exchange rates and several equity series. The model implies
semi-martingale prices and thus precludes arbitrage in a standard
two-asset economy. Volatility has long-memory, and the highest finite
moment of returns can have any value greater than two. The local
variability of the process is characterized by a renormalized
probability density of local Hölder exponents. Unlike standard
models, multifractal paths contain a multiplicity of these exponents
within any time interval. We develop an estimation method, and infer a
parsimonious generating mechanism for the exchange rate series.
Simulated samples replicate the moment-scaling found in the data. |
| URI: | http://hdl.handle.net/2451/27223 |
| Appears in Collections: | Finance Working Papers
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