Modeling ex post variance jumps: implications for density and tail risk forecasting

John Maheu and Efthimios Nikolakopoulos

Quantitative Finance, 2026, vol. 26, issue 2, 161-183

Abstract: This paper focuses on modeling ex post variance jumps including several time-dependent arrival specifications to assess their importance to forecasts of daily returns and variance measures. The benchmark specification for variance measures includes two autoregressive components that capture the persistent and transitory elements. To this we add a jump process with either independent arrival rates, autoregressive conditional jump intensities, or a stochastic autoregressive jump arrival specification. Results from four major markets and four stocks show that ex post variance jumps are frequent and persistent. Modeling time-dependent variance jumps strongly improves ex post variance density forecasts for multiperiod forecast horizons and improves forecasts of the return density. There are economic benefits to modeling variance jumps as well. Models with time-dependent ex post variance jumps improve tail risk forecasting of value-at-risk and expected shortfall.

Date: 2026
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DOI: 10.1080/14697688.2025.2565290

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