Joint Dynamics of Implied Volatility of Liquid DAX Components

Abstract

Implied volatility can be considered as a function of strike level and time to maturity. As it is calculated from the actual trading options, it contains dynamic, multi-dimensional information of options, modelling the implied volatility is an interesting task for researchers. Dynamic semiparametric factor models (DSFM) are used to model the implied volatility surface. It employs semiparametric factor functions and time variate loadings to reduce the dimensions of the data. This master thesis applies joint analysis with the time variate factor loadings resulted from DSFM, in order to discuss the relationship between index options and stock options. The data of DAX index option and its liquid components stock options will be applied in analysis. The result of the joint analysis shows, that the index option has long term relationship with its stock options. It is unlikely to disperse the risk by trading the stock options under the same index.