Mono Underlying Risk Exploration

Abstract

We have seen how to analyze the smile risk. We have learnt how to decompose this risk in a photography risk (fitting the initial smile) and a dynamic risk (capturing elements of its dynamic). Not all products need full exposure to the smile and its dynamic. This question is answered via a progressive approach in which we start by exploring the gamma map. We also compute the smile toxicity index to know if a model extension is necessary. In the most complex case, where the gamma map shows changes of exposure and the presence of an important smile toxicity index, we need to figure out the right mixing weight, the right blending factor issued from a statistical study of the volatility dynamic in the market. We developed a large set of models and approaches for which we have full access, analytically or semianalytically, to their properties.