Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/25039
Authors: 
Fengler, Matthias R.
Härdle, Wolfgang Karl
Mammen, Enno
Year of Publication: 
2005
Series/Report no.: 
SFB 649 discussion paper 2005,020
Abstract: 
A primary goal in modelling the implied volatility surface (IVS) for pricing and hedging 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 modelling bias. We propose a dynamic semiparametric factor model (DSFM), 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 a sticky moneyness model. Finally, based on the DSFM, we devise a generalized vega-hedging strategy for exotic options that are priced in the local volatility framework. The generalized vega-hedging extends the usual approaches employed in the local volatility framework.
Subjects: 
smile
local volatility
generalized additive model
backfitting
functional principal component analysis
JEL: 
C14
G12
Document Type: 
Working Paper

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