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Local volatility of volatility for the VIX market


Drimus, Gabriel Grigore; Farkas, Erich Walter (2013). Local volatility of volatility for the VIX market. Review of Derivatives Research, 16(3):267-293.

Abstract

Following a trend of sustained and accelerated growth, the VIX futures and options market has become a closely followed, active and liquid market. The standard stochastic volatility models—which focus on the modeling of instantaneous variance—are unable to fit the entire term structure of VIX futures as well as the entire VIX options surface. In contrast, we propose to model directly the VIX index, in a mean-reverting local volatility-of-volatility model, which will provide a global fit to the VIX market. We then show how to construct the local volatility-of-volatility surface by adapting the ideas in Carr (Local variance gamma. Bloomberg Quant Research, New York, 2008) and Andreasen and Huge (Risk Mag 76–79, 2011) to a mean-reverting process.

Abstract

Following a trend of sustained and accelerated growth, the VIX futures and options market has become a closely followed, active and liquid market. The standard stochastic volatility models—which focus on the modeling of instantaneous variance—are unable to fit the entire term structure of VIX futures as well as the entire VIX options surface. In contrast, we propose to model directly the VIX index, in a mean-reverting local volatility-of-volatility model, which will provide a global fit to the VIX market. We then show how to construct the local volatility-of-volatility surface by adapting the ideas in Carr (Local variance gamma. Bloomberg Quant Research, New York, 2008) and Andreasen and Huge (Risk Mag 76–79, 2011) to a mean-reverting process.

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Citations

3 citations in Web of Science®
4 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:2013
Deposited On:19 Mar 2013 08:09
Last Modified:05 Apr 2016 16:27
Publisher:Springer
ISSN:1380-6645
Free access at:Official URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s11147-012-9086-9
Official URL:http://link.springer.com/article/10.1007/s11147-012-9086-9
Related URLs:http://www.zora.uzh.ch/55850/
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1970547
Other Identification Number:merlin-id:7941

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