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

This paper examines continuous-time models for the price and volatility processes of individual stocks and the S\amp;P 100 index via Markov Chain Monte Carlo estimation. We find that the stochastic processes governing individual stocks are rather heterogeneous. A key result of our investigation is that index jumps are not necessarily accompanied by jumps in a large number of individual stocks when we apply the same critical values for a posteriori jump probabilities to the index and the stocks. Albeit on a generally lower level of jump probabilities we can nevertheless distinguish between index jump days where the majority of industrial sectors have high jump probabilities and those where this is not the case. We therefore interpret index jumps in the first scenario as 'macro driven', and as 'statistical jumps' otherwise. Concerning diffusive volatility innovations we find that the first principal component is highly correlated with index variance innovations and can therefore be interpreted as a variance market factor