To VaR, or Not to VaR, That is the Question

TL;DR

This paper examines the limitations of traditional VaR models by incorporating market-based probabilities that account for trade volume randomness, highlighting their impact on price volatility predictions and risk assessment accuracy.

Contribution

It introduces market-based probability models that depend on trade volume randomness, contrasting with conventional frequency-based models, and analyzes their effect on volatility predictions.

Findings

Market-based probabilities depend on trade volume randomness.

Trade volume variability limits the accuracy of VaR and volatility forecasts.

Gaussian approximations become less reliable over time due to volume effects.

Abstract

We consider economic obstacles that limit the reliability and accuracy of value-at-risk (VaR). Investors who manage large market transactions should take into account the impact of the randomness of large trade volumes on predictions of price probability and VaR assessments. We introduce market-based probabilities of price and return that depend on the randomness of market trade values and volumes. Contrary to them, the conventional frequency-based price probability describes the case of constant trade volumes. We derive the dependence of market-based price volatility on the volatilities and correlation of trade values and volumes. In the coming years, that will limit the accuracy of price probability predictions to Gaussian approximations, and even the forecasts of market-based price volatility will be inaccurate and highly uncertain.