A Multifractal Model of Asset Returns in the Context of the New Economy Paradigm

The hereto article indicates how multifractals related ideas can contribute to the modelling of the long-memory nature of the financial market volatility. The multifractal models appear in the context of the new paradigm of the financial markets, being related to Benoit Mandelbrot’s fractal view of the financial markets, while the analysed multifractal model was developed by Laurent Calvet and Benoit Mandelbrot and it’s based on the concepts of fat tails and long time dependence or long memory, representing an alternative to ARCH models, focusing on the multi-scaling property of the process, resulting a promising alternative to ARCH models due to scale-consistency. The Multifractal Model of Asset Returns compounds a Brownian motion with a multifractal time-deformation process that produces volatility clustering, and its purpose is not to predict the future with certainty, but to create a more realistic picture of market risks, given the lately delicate situation of the hedge funds, a more accurate estimate of risk being needed. The Multifractal Model of Asset Returns presented in this paper incorporates regularities observed in financial time series, including fat tails and long memory, multifractality being defined by a set of restrictions on the process moments as the time scale of observations changes, integrated in the model through trading time, a random distortion of clock time that accounts for changes in volatility.