11 - Conclusion

Abstract

Markov switching multifractal (MSM) captures thick tails, long-memory features, and intertwined volatility cycles of heterogeneous durations. When volatility components have a discrete distribution, MSM is a latent Markov chain, and its parameters can be estimated by maximizing the closed-form likelihood of the return series. Bayesian updating permits filtering of volatility components, and the Markov construction implies tractable multistep prediction. MSM performs well in-sample, produces good forecasts of volatility, and generates reliable estimates of the value-at-risk in a position or portfolio of assets. The transition between discrete- and continuous-time versions of MSM is remarkably straightforward, which is a substantial operational advantage of our approach. MSM integrates easily into equilibrium models, providing a tractable framework within which to analyze the impact of multifrequency shocks on endogenous asset prices. MSM offers an opportunity to tie together various phenomena that have been previously modeled in isolation. The interaction of shocks with heterogeneous frequencies is a potent source of price dynamics that can explain financial data at all horizons with a very limited number of parameters.