Volatility Index Derivatives

Construction Of the Implied Volatility Smile
Even extremely liquid markets, as the market for European style options on equity indexes, sometimes fail to provide sufficient data for pricing its options, as an example particular options might not be liquid enough. We are investigating an extension of a well-known and widely spread "market-based" Vanna-Volga method, which not only allows to retrieve reasonable estimates for option premiums, but also to determine consistent implied volatilities easily. The theoretical results are then analyzed using the daily settlement prices of the Dow Jones EURO STOXX 50 call options traded at Eurex. Introducing a stochastic volatility model, we were also able to deliver an explanation for the formulas, which were previously heuristically justified merely by formal expansion of the option premium by Itô.

Volatility and its Measurements: The Design of a Volatility Index and the Execution of its Historical Time Series at the Deutsche Börse AG
In April 2005 Stoxx Limited, the Swiss Exchange and Deutsche Börse launched a new family of volatility indexes. To prepare for the launch of new derivative products based on these indexes Eurex strongly supported the development and performed the construction of the historical time series. In this thesis we outline various volatility concepts usable as an underlying and explain which one is most suitable for index construction and forms the basis of the new index family. We outline in detail the actual index construction algorithm and document how the historical time series were evaluated. Finally we perform a first analysis of the historical time series. This analysis can be used as a basis to both develop and understand new volatility derivatives at Eurex.