Title: Nonparametric inference on the self-excitation of jumps in jump diffusion models
Authors: Simon Kwok - University of Sydney (Australia) [presenting]
Abstract: Understanding the jump dynamics of market prices is important for derivative pricing and risk management. Despite their analytical tractability, parametric jump diffusion models entail restrictive and unrealistic structure on the jump dynamics. We propose a set of nonparametric estimator for jump autocorrelation associated with different powers of the log-return process. The nonparametric estimator is consistent for the jump autocorrelation measure and asymptotically normal under mild moment and stationarity conditions. This enables pointwise inference through the construction of jump auto-correlogram with confidence bounds. Furthermore, we study an omnibus test for no self-excitation of jumps at all positive lag orders. The method is naturally extendable to the inference of cross-correlation of jumps in a bivariate setting. In an empirical study of jump contagion in stock markets, we found richer jump dynamic structure that is different from what was implied from conventional jump diffusion models in the literature.