No-Arbitrage Semimartingale Restrictions for Continuous-Time Volatility Models Subject to Leverage Effects, Jumps, and IID Noise: Theory and Testable Distributional Implications

Working Paper: NBER ID: w12963

Authors: Torben G. Andersen; Tim Bollerslev; Dobrislav Dobrev

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.

Keywords: volatility models; leverage effects; jumps; intraday data; nonparametric volatility measures

JEL Codes: C15; C22; C52; C80; G10


Causal Claims Network Graph

Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.


Causal Claims

CauseEffect
presence of jumps (C69)return distribution characteristics (D39)
leverage effects (G41)semimartingale assumption (C51)
jumps and leverage effects (C58)standardized returns (G12)
standardized returns (adjusted for jumps) (G12)IID Gaussian (C26)
model specification (jump-diffusion vs. pure diffusion) (C22)observed return dynamics (C69)
market microstructure noise (G14)findings (Y40)

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