First-passage probability, jump models, and intra-horizon risk

This paper proposes a risk measure, based on first-passage probability, which reflects intra-horizon risk in jump models with finite or infinite jump activity. Our empirical investigation shows, first, that the proposed risk measure consistently exceeds the benchmark value-at-risk (VaR). Second, jump risk tends to amplify intra-horizon risk. Third, we find large variation in our risk measure across jump models, indicative of model risk. Fourth, among the jump models we consider, the finite-moment log-stable model provides the most conservative risk estimates. Fifth, imposing more stringent VaR levels accentuates the impact of intra-horizon risk in jump models. Finally, using an alternative benchmark VaR does not dilute the role of intra-horizon risk. Overall, we contribute by showing that ignoring intra-horizon risk can lead to underestimation of risk exposures.