Jump Intensities, Jump Sizes, and the Relative Stock Price Level

Large stock price movements are modeled as jumps in the stochastic processes of stock prices. In the current literature, the jump intensity is typically specified in models as a function of the current diffusive volatility and past jump intensities, while the jump size is assumed to be independent of the jump intensity. We use a nonparametric jump detection test to identify jumps in several stock indexes and examine the determinants of the jump intensity and the jump size. We find little evidence that the jump intensity depends on the current diffusive volatility. Instead, the jump intensity and the jump size depend on the current stock price level relative to its historical average, beside past jump intensities. The results in this paper provide new perspectives for modeling jumps in the theory of options pricing and in the applications of risk management.