Crisis risk prediction with concavity from Polymodel

<p style='text-indent:20px;'>Financial crises are an important research topic because of their impact on the economy, businesses, and populations. However, prior research tends to generate reactive systemic risk measures, in the sense that the measure surges after the crisis starts. Few of them succeed in warning of financial crises in advance. In this paper, we first sketch a toy model that produces normal mixture distributions based on a dynamic regime switching model. We derive that the relative concavity among various indices tends to increase before a crisis. Using Polymodel theory, we introduce a measure of concavity as a crisis risk indicator, and test it against known crises observed in the past. We validate this indicator by a trading strategy holding long or short positions on the S &amp; P 500 Index, depending on the indicator value.</p>