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Fengler, Matthias R.
Härdle, Wolfgang
Mammen, Enno
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Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 2003,54
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 näive trader models. The model can be a backbone in risk management serving for value at risk computations and scenario analysis.
Implied Volatility Surface
Generalized Additive Models
Functional Principal Component Analysis
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Working Paper

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