@techreport{Fengler2005dynamic,
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.},
address = {Berlin},
author = {Matthias R. Fengler and Wolfgang Karl H\"{a}rdle and Enno Mammen},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {C14; G12; 330; smile; local volatility; generalized additive model; backfitting; functional principal component analysis},
language = {eng},
number = {2005,020},
publisher = {SFB 649, Economic Risk},
title = {A dynamic semiparametric factor model for implied volatility string dynamics},
type = {SFB 649 discussion paper},
url = {http://hdl.handle.net/10419/25039},
year = {2005}
}
