A Brief Study of the Multifractal Model of Asset Returns.

Abstract: Understanding the processes that determine price variations is important in evaluating risks in the financial system. Many of the conventional models used to describe price variations are based on the model of Brownian motion. This model fails to take into account large price deviations, dependence and clustering that are present in financial markets. This thesis attempts to explain an alternative method, the Multifractal Model of Asset Returns (MMAR), based mainly on the three papers published by Mandelbrot, Fisher and Calvet in 1997. MMAR allows for large price deviations, clustering and dependence of price variation. In this thesis, the theoretical framework of MMAR is covered and some empirical tests are then carried out on the JPY/USD and SEK/USD exchange rate to show the faults of the conventional model and to examine the validity of the MMAR. The Hurst exponents of the exchange rates are estimated and the results seem to indicate there are some signs of multifractality for the JPY/USD rate. It is however difficult to measure the value of the MMAR in relationship to the complexity it brings.