Correlation, Where are You? Where are We? Update on Correlation Modeling

Abstract

During the first decades following Black and Scholes, the quantitative finance have been focus mainly on the modeling of the volatility. Indeed, the expansion of derivatives product brought some liquidity regarding this parameter. The implied volatility is the reflect of market convention for the vanilla premium but are also an extension of the industry focus. If the volatility modelling is difficult, the correlation modelling stage at another level. In fact, many market participant portfolios were attached to correlation risk - market participants such as insurance companies and pension funds - therefore, banks innovated solutions which imply transfer of the risk. A huge range of products such as Dispersion, Correlation Swap, Basket Option, Best Of and Worst Of have been introduced and sold with more or less popularity. Banks were willing to take the risk but they needed more elaborate model in order to capture the correlation risk. If the business pressure was to trade and deal with the residual risk with conventional correlation framework (deterministic term structure), after the default of Lehman Brother, the Trading Desk had to transfer the pressure and challenge quants in order to have the ability to hedge their correlation exposure. In this paper, we enumerate industry innovations on correlation modeling and discuss some improvements and market understanding of it.