Investigating Impacts of Self-Exciting Jumps in Returns and Volatility: A Bayesian Learning Approach

Abstract:     
The paper proposes a new class of continuous-time asset pricing models where negative jumps play a crucial role. Whenever there is a negative jump in asset returns, it is simultaneously passed on to diffusion variance and the jump intensity, generating self-exciting co-jumps of prices and volatility and jump clustering. To properly deal with parameter uncertainty and hindsight bias, we employ a Bayesian learning approach, which generates all quantities necessary for sequential real-time model analysis. Empirical investigation using S&P 500 index returns shows that volatility jumps at the same time as negative jumps in asset returns mainly through jumps in diffusion volatility. We find weak evidence for jump clustering. Learning and parameter uncertainty are shown to have important implications for risk management, option pricing and volatility forecasting.

Number of Pages in PDF File: 55

Keywords: Extreme Events, Self-Excitation, Volatility Jump, Jump Clustering, Parameter Learning, Sequential Bayes Factor, Risk Management, Option Pricing, Volatility Forecasting

JEL Classification: C11, C13, C32, G12

working papers series