Price and volatility jumps in the stock market

Abstract

Chapter1: We study the bivariate jump process involving the S&P 500 and the Euro Stoxx 50 index with jumps extracted from high frequency data using non-parametric methods. Our analysis, based on the generalized Hawkes process, reveals the presence of self excitation in the jump activity which is responsible for jump clustering but has a very small persistence in time. Concerning cross-market effects, we find statistically significant co-jumps occurring when both markets are simultaneously operating but no evidence of contagion in the jump activity, suggesting that the role of jumps in volatility transmission is negligible. Moreover, we find a negative relationship between the jump activity and the continuous volatility indicating that jumps are mostly detected during tranquil market conditions rather than in periods of stress. Importantly, our empirical results are robust under different jump detection methods.

Chapter2:We construct new nonparametric robust to jumps estimators for the realized volatility combining multiple measures applied to high frequency data. Collecting information from several estimators, this method provides a higher asymptotic efficiency and allows to improve finite sample properties. We use the new estimators to construct nonparametric tests for the detection of jumps in asset prices: our Monte Carlo study shows that such tests can achieve substantially more power compared to other common tests.

Chapter3:We introduce a new stochastic process generalizing the Autoregressive Gamma (ARG ) of [Gourieroux_Jasiak_2006]. This process is based on a new and more flexible specification of the conditional distribution which extends the non-central gamma while preserving the same analytical tractability. We propose an empirical a application to the realized volatility measured from high frequency data. The period of our analysis includes the sub-prime and the Euro Sovereign crisis. Our results highlight the superior performances of the new process compared the standard ARG and confirm the need of at least two stochastic factors for a satisfactory description of the volatility dynamics: one factor is responsible for small volatility fluctuations while the second factor generates large upward shocks featuring volatility jumps.