Implied volatility is one of the key issues in modern quantitative finance, since plain vanilla option prices contain vital information for pricing and hedging of exotic and illiquid options. European plain vanilla options are nowadays widely traded, which results in a great amount of...

A primary goal in modelling the implied volatility surface (IVS) for pricing andhedging aims at reducing complexity. For this purpose one fits the IVS each dayand applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of...

The pricing accuracy and pricing performance of local volatility models crucially depends on absence of arbitrage in the implied volatility surface: an input implied volatility surface that is not arbitrage-free invariably results in negative transition probabilities and/ or negative local...

We investigate the relationship between inflation and price variation using highly disaggregated, weekly price data for consumption goods recorded in Germany during 1995, a low inflation period. We find a significant positive correlation between the rates of price change and price dispersion,...

It is common practice to identify the number and sources of shocks that move implied volatilities across space and time by applying Principal Components Analysis (PCA) to pooled covariance matrices of changes in implied volatilities. This approach, however, is likely to result in a loss of...

The analysis of volatility in financial markets has become a first rank issue in modern financial theory and practice: Whether in risk management, portfolio hedging, or option pricing, we need to have a precise notion of the market's expectation of volatility. Much research has been done on the...

Multivariate Volatility Models belong to the class of nonlinear models for financial data. Here we want to focus on multivariate GARCH models. These models assume that the variance of the innovation distribution follows a time dependent process conditional on information which is generated by...