A Wavelet Approach to Tail Risk

Abstract

We apply wavelet analysis to observe financial returns. We demonstrate how useful wavelets can be to separate normal market conditions from stressed market conditions. After noise removal, a process appears to manifest itself during period of financial distress and show a remarkable alignment across asset classes. We finally propose an adaptation of a hidden Markov model used in speech recognition for the simulation of financial returns in the wavelet domain. This model natively acknowledges that daily returns contain different frequency information, simulates realistically over a given risk horizon and captures the tail risk: wild movements unanticipated by usual normality assumptions.