HMM based scenario generation for an investment optimisation problem

The Geometric Brownian motion (GBM) is a standard method for modeling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, GBM has been considered unable to properly capture important features, like extreme behaviour or volatility clustering. We propose an approach by which, the parameters of the GBM follow a regime switching model, more precisely a hidden Markov model (HMM). Thus, financial time series are modeled via a hidden Markov model (HMM) with a GBM in each state. Using this approach, we generate scenarios for a financial portfolio optimisation problem in which the portfolio CVaR is minimised. Numerical results are presented.