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Wagner, N., Szimayer, A. Alternative Model Specifications for Implied Volatility Measured by the German VDAX. Credit and Capital Markets – Kredit und Kapital, 34(4), 590-618. https://doi.org/10.3790/ccm.34.4.590
Wagner, Niklas and Szimayer, Alexander "Alternative Model Specifications for Implied Volatility Measured by the German VDAX" Credit and Capital Markets – Kredit und Kapital 34.4, 2001, 590-618. https://doi.org/10.3790/ccm.34.4.590
Wagner, Niklas/Szimayer, Alexander (2001): Alternative Model Specifications for Implied Volatility Measured by the German VDAX, in: Credit and Capital Markets – Kredit und Kapital, vol. 34, iss. 4, 590-618, [online] https://doi.org/10.3790/ccm.34.4.590
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Alternative Model Specifications for Implied Volatility Measured by the German VDAX

Wagner, Niklas | Szimayer, Alexander

Credit and Capital Markets – Kredit und Kapital, Vol. 34 (2001), Iss. 4 : pp. 590–618

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Article Details

Publisher Name
Duncker & Humblot
DOI
https://doi.org/10.3790/ccm.34.4.590
Language
Multiple languages
Pages
29

Author Details

Niklas Wagner, Dresden/Berkeley

Alexander Szimayer, Bonn

References

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Abstract

Alternative Model Specifications for Implied Volatility Measured by the German VDAX

In this paper, two nested model specifications for the stochastic behavior of the German stock market volatility index VDAX are compared based on a sample of index observations. Following the literature, the well-known mean reverting diffusion model serves as the standard model specification. The second model specification is an extension which allows for discontinuous changes in the series. The estimation results for the VDAX indicate that the empirical observations do not confirm the moment restrictions given by the standard model. While, at the given confidence level, this yields to a rejection of the mean reverting diffusion model, the extended specification cannot be rejected providing significant evidence of a positive jump component. An application of the mean reverting jump diffusion model is given in a risk-neutral option pricing framework. Simulated option prices reveal economically and statistically significant price differences not only depending on the choice of the model specification but also due to the consideration of the jump component itself. (JEL C13, C15, C22, G13)

Table of Contents

Section Title Page Action Price
Niklas Wagner/Alexander Szimayer: Alternative Model Specifications for Implied Volatility\rMeasured by the German VDAX 590
I. Introduction 590
II. Alternative Volatility Model Specifications 592
1. Mean Reverting Jump Diffusion 592
2. Mean Reverting Diffusion 593
3. A Comparison of the Model Specifications 593
4. Empirical Studies 594
III. Model Estimation 595
1. Discretization of the Model 595
2. On the Choice of the Moment Restrictions 596
3. Specification of the Moment Restrictions 597
4. Estimation, Asymptotics, and Test Procedures 598
IV. Empirical Results 600
1. The Data Sample 600
2. Calculation of the Estimates 601
3. Estimation Results 602
4. Results for Alternative Estimation Approaches 605
V. Option Pricing Under Risk Neutrality 606
1. Preliminaries 607
2. Simulated Call Option Prices 608
3. Pricing Implications of the Jump Component 613
VI. Conclusion 615
References 615
Summary: Alternative Model Specifications for Implied Volatility Measured by the German VDAX 617
Zusammenfassung: Zur Modellierung des VDAX-Volatilitätsindexes 617
Résumé: Modèles alternatifs pour la volatilité mesurée par l'indice allemand VDAX 618

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