The Fine Structure of Asset Returns: An Empirical Investigation

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Abstract
We investigate the relative importance of di®usion and jumps in a new jump di®usion model for asset returns. In contrast to the standard modelling of jumps for asset returns, the jump component of our process can displaynite or innite activity, andnite or innite variation. Empirical investigations of time series indicate that index dynamics are essentially devoid of a di®usion component, while this component may be present in the dynamics of individual stocks. This result leads to the conjecture that the risk-neutral process should be free of a di®usion component for both indices and individual stocks. Empirical investigation of options data tends to conrm this conjecture. We conclude that the statistical and risk-neutral processes for indices and stocks tend to be pure jump processes of innite activity andnite variation.