This paper revisits the fractional co-integrating relationship between ex-ante implied volatility and ex-post realized volatility. Previous studies on stock index options have found biases and inefficiencies in implied volatility as a forecast of future volatility. It is argued that the concept...

This paper revisits the fractional co-integrating relationship between ex-ante implied volatility and ex-post realized volatility. Previous studies on stock index options have found biases and inefficiencies in implied volatility as a forecast of future volatility. It is argued that the concept...

This paper introduces the Markov-Switching Multifractal Duration (MSMD) model by adapting the MSM stochastic volatility model of Calvet and Fisher (2004) to the duration setting. Although the MSMD process is exponential ß-mixing as we show in the paper, it is capable of generating highly...

This paper introduces the Markov-Switching Multifractal Duration (MSMD) model by adapting the MSM stochastic volatility model of Calvet and Fisher (2004) to the duration setting. Although the MSMD process is exponential ß-mixing as we show in the paper, it is capable of generating highly...

This paper develops a two-step estimation methodology that allows us to apply catastrophe theory to stock market returns with time-varying volatility and to model stock market crashes. In the first step, we utilize high-frequency data to estimate daily realized volatility from returns. Then, we...