We extend the Markov Switching Multifractal (MSM) framework of Calvet and Fisher (2004) by introducing leverage and skewness (LS). The resulting MSM--LS model preserves the tractability of the original MSM specification while allowing for time-varying leverage and skewness in returns, two salient empirical features that are pervasive in financial time series. We further show that the MSM--LS model delivers superior volatility forecasts across multiple horizons, highlighting the economic value of incorporating leverage and skewness into the multifractal volatility framework.
