Arbeitspapier

A dynamic semiparametric factor model for implied volatility string dynamics

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.

Language
Englisch

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

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

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

Handle
Last update
20.09.2024, 8:25 AM CEST

Data provider

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Object type

  • Arbeitspapier

Associated

  • Fengler, Matthias R.
  • Härdle, Wolfgang Karl
  • Mammen, Enno
  • Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk

Time of origin

  • 2005

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