Applying the Multifractal Model of Asset Returns (MMAR) to Financial Markets: Insights and Limitations

This study presents an application of fractal mathematics to financial markets through the utilization of the Multifractal Model of Asset Returns (MMAR). The model is employed to analyse a 30-year dataset encompassing three distinct financial markets: the USD/NOK currency pair, the OMXS30 stock index, and the 12-month LIBOR rate. The MMAR model successfully captures essential stylized facts about financial markets, including high kurtosis, non-independent price movements, and clustered volatile days. Simulations generated by the model demonstrate realistic behaviour and multifractal characteristics. However, the model lacks a statistical method for assessing its accuracy and may underestimate kurtosis in high-kurtosis markets. Notably, the model is capable of producing simulations across a wide range of kurtosis values and can be instrumental in stress-testing portfolios. Despite its potential, the model is subject to limitations, such as the need for human judgment, ambiguous predictions, and interpretability issues. Furthermore, the model may become unreliable following a high-kurtosis event.