VaR for the day you can't sell

Value-at-Risk answers a specific question — how much could this position lose? — and it quietly assumes you can actually sell the position at something close to the observed market price if you need to. That assumption is exactly what breaks during a real crisis, and this paper builds a risk measure aimed squarely at the assumption itself rather than at price moves.

Illiquidity gets a name of its own

The authors introduce Illiquidity-at-Risk, or IlliQaR: a tail-risk measure built to estimate extreme liquidity dry-ups, the kind of episode where a market doesn't just move against you but becomes very hard to trade in at all. It is built on the realized Amihud measure — a well-established illiquidity metric computed from high-frequency data as the ratio of realized volatility to trading volume, so it rises when price impact per unit of volume spikes. The paper then compares a range of linear and nonlinear forecasting models for that quantity, with a specific focus on one modelling choice: whether to let illiquidity jump discontinuously, or force it to evolve smoothly.

The jump is the whole finding

That modelling choice turns out to matter enormously. Models that treat liquidity dynamics as continuous — evolving smoothly period to period — systematically underestimate how severe liquidity evaporation can get during genuine stress. Explicitly modelling jumps in liquidity materially improves probability coverage precisely in the stressed periods where it counts, which is another way of saying: the moments when you most need your risk model to be right are the moments a smooth model is most likely to be quietly wrong.

Liquidity crises don't unfold smoothly — and a model that assumes they do will underestimate exactly the dry-ups that matter most.

A systemic signature, not just a stock-by-stock one

The empirical analysis runs across the S&P 500 index and a cross-section of 25 major U.S. equities. The finding that gives the paper its sharper edge: individual-stock IlliQaR breaches don't happen in isolation — they cluster around periods of S&P 500-level liquidity stress. In other words, when the broad market's liquidity dries up, individual names are far more likely to be experiencing their own extreme illiquidity events at the same time. That clustering is the signature of a systemic, not merely idiosyncratic, phenomenon, and it means the index itself can act as a leading indicator for illiquidity risk building up underneath it in individual names.

Why this deserves to sit next to VaR, not inside it

The natural objection is that liquidity risk is already implicitly baked into volatility-based risk measures. This paper's answer is that it isn't captured well enough, because volatility and tradability can diverge — a position can have a perfectly survivable price VaR while becoming disproportionately expensive to actually unwind, and a generic volatility number won't tell you which situation you're in. Giving illiquidity its own explicit, jump-aware tail-risk quantity means a fund can track "how much could this fall" and "how expensive could this become to exit" as genuinely separate questions, rather than hoping one metric quietly covers both.

Honest caveats

The analysis is built on realized Amihud, which is a well-regarded proxy for illiquidity but a proxy nonetheless — it is not a direct measure of executable trade size or actual market depth. The empirical scope is U.S. large caps and the S&P 500 specifically; how the jump-clustering pattern behaves in less liquid asset classes, smaller-cap names, or non-U.S. markets is an open question the paper doesn't address. And as with most tail-risk work, backtesting a measure designed to flag rare, extreme events is inherently data-constrained — genuinely severe liquidity crises are, thankfully, infrequent, which limits how much any historical sample can say about the far tail.

Why it matters

For anyone setting liquidation limits, sizing margin, or stress-testing a trading book, the practical upgrade here is concrete: run return VaR, expected shortfall, and Illiquidity-at-Risk side by side, rather than assuming the first two already tell you what you need to know about the third. The clustering finding gives risk teams and market-makers something actionable — S&P 500 liquidity stress as an early-warning signal for illiquidity building up in specific names — and for regulators and exchanges thinking about systemic risk, a jump-aware, index-linked view of illiquidity dry-ups is a more honest picture of how liquidity crises actually propagate than treating each stock's tradability as its own isolated concern.