Where Volume Belongs in a Tail Risk Model: Extreme Quantile Forecasts, Subordination, and Market Depth

Ahmad Shauqi bin Haji Mohamad Zubir and Muhammad Luqman bin Mohd Nasir

MPRA Paper from University Library of Munich, Germany

Abstract: Trading volume has forecast volatility in half a century of research, yet risk models hold capital at extreme quantiles the volume literature never scores. We evaluate the expected and unexpected components of trading volume inside a layered tail risk architecture, a volatility filter beneath an extreme value model for standardized exceedances, for 300 liquid Bursa Malaysia firms over 467,148 evaluation days from 2018 to 2025, with every model re-estimated annually in real time and forecasts ranked by strictly consistent scoring functions. Four results emerge. Unexpected volume improves 99th and 99.5th percentile forecasts by about a tenth of a percent of the quantile loss, on 58 percent of days, at unchanged coverage and capital, robust to a pre-committed battery including a full pipeline permutation placebo. The signal is layer specific: surprise volume works entirely through the volatility filter and adds nothing to the exceedance scale at any threshold, the exclusion that return subordination implies, while expected volume compresses the extreme tail from within, the signature of market depth. The gains concentrate in 2021 through 2025, dating the signal's value to a documented transformation of the trading environment. And direct censored likelihood quantification shows this market's price limits shift implied extreme quantiles by half a basis point, licensing standard architectures by measurement rather than assumption. Volume belongs in risk systems, in a specific place, at a measurable price.

Keywords: Trading volume; Value at risk; Extreme value theory; Forecast evaluation; Market depth; Price limits (search for similar items in EconPapers)
JEL-codes: C1 G12 (search for similar items in EconPapers)
Date: 2026-07-22
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