scholarly journals Continuous-Time Skewed Multifractal Processes as a Model for Financial Returns

2012 ◽  
Vol 49 (02) ◽  
pp. 482-502 ◽  
Author(s):  
Emmanuel Bacry ◽  
Laurent Duvernet ◽  
Jean-François Muzy
Keyword(s):  
Continuous Time ◽  
Natural Extension ◽  
Real Data ◽  
Continuous Time Model ◽  
Time Model ◽  
Odd Order ◽  
Multifractal Scaling ◽  
Multifractal Random Walk ◽  
Continuous Time Stochastic Process ◽  
Exact Scaling

We present the construction of a continuous-time stochastic process which has moments that satisfy an exact scaling relation, including odd-order moments. It is based on a natural extension of the multifractal random walk construction described in Bacry and Muzy (2003). This allows us to propose a continuous-time model for the price of a financial asset that reflects most major stylized facts observed on real data, including asymmetry and multifractal scaling.

scholarly journals Continuous-Time Skewed Multifractal Processes as a Model for Financial Returns

2012 ◽  
Vol 49 (2) ◽  
pp. 482-502 ◽  
Author(s):  
Emmanuel Bacry ◽  
Laurent Duvernet ◽  
Jean-François Muzy
Keyword(s):  
Continuous Time ◽  
Natural Extension ◽  
Real Data ◽  
Continuous Time Model ◽  
Time Model ◽  
Odd Order ◽  
Multifractal Scaling ◽  
Multifractal Random Walk ◽  
Continuous Time Stochastic Process ◽  
Exact Scaling

We present the construction of a continuous-time stochastic process which has moments that satisfy an exact scaling relation, including odd-order moments. It is based on a natural extension of the multifractal random walk construction described in Bacry and Muzy (2003). This allows us to propose a continuous-time model for the price of a financial asset that reflects most major stylized facts observed on real data, including asymmetry and multifractal scaling.

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