No-Arbitrage Semi-Martingale Restrictions for Continuous-Time Volatility Models subject to Leverage Effects and Jumps: Theory and Testable Distributional Implications*

We shed light on the characteristics of high-frequency asset return and volatility processes and their implications for daily return distributions. We document that the standard jumpdiffusion setting readily accommodates the main features of equity index returns, including stochastic volatility, outlier behavior and a strong asymmetry between return and volatility innovations. We also informally test, and confirm, that the underlying high-frequency returns are consistent with the general semi-martingale restriction by recovering almost exact Gaussianity of the “daily” returns sampled in “financial time” through a dynamic correction for jumps and an “event-time” sampling scheme. Each step of the procedure provides insights into the corresponding aspect of the data: jumps, stochastic volatility and the asymmetry or “leverage effect”. Please send email to Mathias Drton ([email protected]) for further information. Information about building access for persons with disabilities may be obtained in advance by calling the department office at (773) 702-8333.