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Implied volatility string dynamics

Matthias Fengler (), Wolfgang Härdle () and Enno Mammen

No 2003,54, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: 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.

Keywords: Implied Volatility Surface; Smile; Generalized Additive Models; Backfitting; Functional Principal Component Analysis (search for similar items in EconPapers)
JEL-codes: C14 G12 (search for similar items in EconPapers)
Date: 2003
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