Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach

This paper reports a new methodology and results on the forecast of the numerical value of the fat tail(s) in asset returns distributions using the irrational fractional Brownian motion model. Optimal model parameter values are obtained from fits to consecutive daily 2-year period returns of S&P500 index over [1950-2016], generating 33-time series estimations. Through an econometric model, the kurtosis of returns distributions is modelled as a function of these parameters. Subsequently an auto-regressive analysis on these parameters advances the modelling and forecasting of kurtosis and returns distributions, providing the accurate shape of returns distributions and measurement of Value at Risk.

Automated summary

This study introduces a new methodology using the irrational fractional Brownian motion model to forecast the numerical value of the fat tail(s) in asset returns distributions. By fitting parameter values to consecutive daily 2-year period returns of the S&P500 index over [1950-2016], optimal model parameter values are obtained, leading to 33-time series estimations. Through an econometric model and auto-regressive analysis, the kurtosis and returns distributions are modeled and forecasted, providing accurate measurements of return distribution shapes and Value at Risk.