Measuring risk in an explosive environment

Financial asset bubbles can be characterized by periods of expansion and collapse. Expansions are often modeled as explosive processes for the asset price. Ignoring such explosiveness leads to misspecified Value-at-Risk (VaR) and related measures, e.g. Expected Shortfall. Considering an explosive autoregressive model. We find that the unadjusted down-side VaR is overestimated in explosive periods and also misspecified during the collapse. The form of the misspecification strongly depends on several factors: (i) horizon of the VaR forecast, (ii) duration and strength of the explosive regime (as measured by the length of the explosive subsample and the explosive root), and (iii) the nature of the collapse. The size of the effects (in terms of capital requirements) are quantified by means of an extensive Monte Carlo simulation study. We propose a correction term to be added to the VaR which accounts for the unexpected loss due to a burst. In our empirical applications, we demonstrate the merits and limits of the suggested VaR adjustments, which have to be taken into account for management purposes.