A Jumping Index of Jumping Stocks? An MCMC Analysis of Continuous-Time Models for Individual Stocks

Abstract

This paper examines continuous-time models for the S&P 100 index and its constituents. We find that the jump process of the typical stock looks significantly different than that of the index. Most importantly, the average size of a jumps in the returns of the typical stock is positive, while it is negative for the index. Furthermore, the estimates of the parameters for the stochastic processes exhibit pronounced heterogeneity in the cross- section of stocks. For example, we find that the jump size in returns decrease for larger companies. Finally, we find that a jump in the index is not necessarily accompanied by a large number of contemporaneous jumps in its constituents stocks. Indeed, we find index jump days on which only one index constituent also jumps. As a consequence, we show that index jumps can be classified as induced by either synchronous price movements of individual stocks or macroeconomic events.

Keywords: Jump-diffusion models; individual stocks; Markov Chain Monte Carlo

JEL Classification: G11, G12