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

We consider the core problems of the conventional value-at-risk (VaR) based on the price probability determined by frequencies of trades at a price p during an averaging time interval Δ. To protect investors from risks of market price change, VaR should use price probability determined by the market trade time-series. To match the market stochasticity we introduce the new market-based price probability measure entirely determined by probabilities of random market time-series of the trade value and volume. The distinctions between the market-based and frequency-based price probabilities result different assessments of VaR and thus can cause excess losses. Predictions of the market-based price probability at horizon T equal the forecasts of the market trade value and volume probability measures.