Michael Johannes

State Dependent Jump Models: How Do U.S. Equity Markets Jump?

Coauthor(s): Rohit Kumar, Nicholas Polson.

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Abstract:
This paper introduces a class of state dependent jump (SDJ) models in which the arrival intensity and jump sizes depend on a given set of state variables, including lagged jumps. With this model, we investigate the structure of jumps to U.S. equity indices, concentrating on the predictability of jumps times if found for all of the indices considered: Standard and Poor's 500 and Mid-Cap, the Russell 1000, 2000, and 3000 indices, the Wilshire 5000 and the Nasdaq 100 (NDX). Given the evidence for predictability, we show how risk management decision are affected by state dependent jump structures. Using inferred jump times and sizes, we also detail the shortcomings of popular jump models and demonstrate how jump models fit various events such as the Crash of 1987. Using implied volatility data, we investigate the ability of implied volatility to predict both jump times and sizes and find strong evidence that implied volatility can predict both jump times and sizes.

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