Dynamik der Fristenstruktur der impliziten Volatilitäten

Using a principal component analysis we investigate the dynamic relations within the term structure of volatilities implied in options on the Swiss Market Index (SMI). It is shown that approximately 99% of the over-all variation of the term structure can be explained by three independent state variables. The first among them describing a level-effect, the second a twist of the term structure and the third influencing its curvature. We demonstrate that risk management concepts and regulations that build primarily on parallel shifts of the term structure of implied volatilities end up with essentially useless results. Using a case study of a book of vega-risks we demonstrate how dramatic these distortions may be if the true correlations within the term structure are neglected. These insights have important regulatory consequences.