This article develops a new conditional jump model to study jump dynamics in stock market returns. We propose a simple filter to infer ex post the distribution of jumps. This permits construction of the shock affecting the time t conditional jump intensity and is the main input into an autoregressive conditional jump intensity model. The model allows the conditional jump intensity to be time-varying and follows an approximate autoregressive moving average (ARMA) form. The time series characteristics of 72 years of daily stock returns are analyzed using the jump model coupled with a generalized autoregressive conditional heteroscedasticity (GARCH) specification of volatility. We find significant time variation in the conditional jump intensity and evidence of time variation in the jump size distribution. The conditional jump dynamics contribute to good in-sample and out-of-sample fits to stock market volatility and capture the rally often observed in equity markets following a significant downturn.
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