No-Arbitrage Semi-Martingale Restrictions for Continuous-Time Volatility Models subject to Leverage Effects, Jumps and i.i.d. Noise: Theory and Testable Distributional Implications

Abstract

We develop a sequential procedure to test the adequacy of jump-diffusion models for return distributions.We rely on intraday data and nonparametric volatility measures, along with a new jump detection technique and appropriate conditional moment tests, for assessing the import of jumps and leverage effects.A novel robust-to-jumps approach is utilized to alleviate microstructure frictions for realized volatility estimation.Size and power of the procedure are explored through Monte Carlo methods.Our empirical findings support the jump-diffusive representation for S&P500 futures returns but reveal it is critical to account for leverage effects and jumps to maintain the underlying semi-martingale assumption.

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