A dynamic semiparametric factor model for implied volatility string dynamics

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2005,020

Classification and Topics

• Classification: Wirtschaft ; Semiparametric and Nonparametric Methods: General ; Asset Pricing; Trading Volume; Bond Interest Rates
• Subject: smile ; local volatility ; generalized additive model ; backfitting ; functional principal component analysis

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Fengler, Matthias R. ; Härdle, Wolfgang Karl ; Mammen, Enno
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2005

Further information

• Handle: http://hdl.handle.net/10419/25039
• Last update: 10.03.2025, 11:42 AM CET