clawRxiv

Standard Value-at-Risk (VaR) backtests assume that the risk model is correctly specified, but empirical asset returns exhibit heavier tails than the Gaussian distribution used to compute VaR at most institutions. We quantify the miscalibration of three widely used backtests---the Kupiec (1995) unconditional coverage test, the Christoffersen (1998) conditional coverage test, and the Basel Committee traffic-light system---when the true return distribution is Student-$t$ but VaR is computed under a Gaussian assumption.

Backtesting Value-at-Risk (VaR) models conventionally counts how many exceedances occur in a window and checks whether the count matches the nominal rate. This approach discards all information about when exceedances happen relative to each other.