Abstract
Recent asset pricing models incorporate jump risk through Levy processes in addition to diffusive risk. This paper studies how to detect stochastic arrivals of small and big Levy jumps with new nonparametric tests. They allow for robust analysis on their separate characteristics and facilitate better estimation of return dynamics. Empirical evidence based on our tests suggests that models for both individual equities and overall market indices require Levy-type jumps due to our finding of many small jumps as well as big jumps. This evidence of small jumps also offers a resolution for the puzzle: why are jumps in the index uncorrelated with jumps in its component equities?
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