Implied volatility string dynamics - Matthias R. Fengler; Wolfgang Härdle; Enno Mammen (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 2003)
A primary goal in modelling the dynamics of implied volatility surfaces (IVS) aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the implied volatility data and may result in a severe modelling bias. We propose a dynamic semiparametric factor model, which approximates the IVS in a finite dimensional function space. The key feature is that we only fit in the local neighborhood of the design points. Our approach is a combination of methods from functional principal component analysis and backfitting techniques for additive models. The model is found to have an approximate 10% better performance than the typical naïve trader models. The model can be a backbone in risk management serving for value at risk computations and scenario analysis.
urn:nbn:de:kobv:11-10050885
Keywords: C14; G12; 330; Implied Volatility Surface; Smile; Generalized Additive Models; Backfitting; Functional Principal Component Analysis