Detecting jumps from Lévy jump diffusion processes

Recent asset-pricing models incorporate jump risk through Lévy processes in addition to diffusive risk. This paper studies how to detect stochastic arrivals of small and big Lévy jumps with new nonparametric tests. The tests allow for robust analysis of their separate characteristics and facilitate better estimation of return dynamics. Empirical evidence of both small and big jumps based on these tests suggests that models for individual equities and overall market indices require incorporating Lévy-type jumps. The evidence of small jumps also helps explain why jumps in the market index are uncorrelated with jumps in its component equities.