A Compound Multifractal Model for High-Frequency Asset Returns

WThis paper builds a model of high-frequency equity returns in clock time by separately modeling the dynamics of trade-time returns and trade arrivals. Our main contributions are threefold. First, we characterize the distributional behavior of high-frequency asset returns both in clock time and trade time and show that when controlling for pre-scheduled market news events, trade-time returns are well characterized by a Gaussian distribution at very fine time scales. Second, we develop a structured and parsimonious model of clock-time returns by subordinating a trade-time Gaussian distribution with a trade arrival process that is associated with a modified Markov-Switching Multifractal Duration (MSMD) model of Chen et al. (2013). Our modification of the MSMD model provides a much better characterization of high-frequency inter-trade durations than the original model of Chen et al. (2013). Over-dispersion in this distribution of inter-trade durations leads to leptokurtosis and volatility clustering in clock-time returns, even when trade-time returns are Gaussian. Finally, we use our model to extrapolate the empirical relationship between trade rate and volatility in an effort to understand conditions of market failure. Our model finds that physical separation of financial markets maintains a natural ceiling on systemic volatility and promotes market stability.