Many Small Jumps or Fat Tails? The Near Jump-Diffusion Paradigm

Abstract

The recent literature on high frequency data highlighted the presence and importance of jumps in asset prices and volatility. However, the empirical findings suggest that there are much more jumps than indicated by parametric models based on daily data (stocks and options), which leads some authors to do tests at an extreme level (0.1%) in order to reduce the number of days with jumps (Andersen, Bollerslev, and Diebold (2007), Huang and Tauchen (2005)). The paper has two contributions. We propose a new approach for testing jumps which indeed leads to the reduction of the number of jumps, providing a theoretical foundation for the approach in Andersen, Bollerslev, and Diebold (2007), Huang and Tauchen (2005). We also prove that the current literature overestimates the magnitude of the contribution of the jumps to the quadratic variation of the stock prices.