Consistent Modeling of VIX and Equity Derivatives Using a 3/2 Plus Jumps Model
In this paper quasi-closed-form solutions are derived for the price of equity and VIX derivatives under the assumption that the underlying follows a 3/2 process with jumps in the index. The newly-found formulae allow for an empirical analysis to be performed. In the case of the pure-diffusion 3/2 model, the dynamics are rich enough to capture the observed upward-sloping implied-volatility skew in VIX options. This observation contradicts a common perception in the literature that jumps are required for the consistent modeling of equity and VIX derivatives. We find that the 3/2 plus jumps model is more parsimonious than competing models from its class; it is able to accurately capture the joint dynamics of equity and VIX derivatives, without sacrificing analytic tractability. The model produces a good short-term fit to the implied volatility of index options due to the richer dynamics, while retaining the analytic tractability of its pure-diffusion counterpart.
|Date of creation:||01 Mar 2012|
|Date of revision:|
|Publication status:||Published as: Baldeaux, J. and Badran, A., 2014, "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model", Applied Mathematical Finance, 21(4), 299-312.|
|Contact details of provider:|| Postal: PO Box 123, Broadway, NSW 2007, Australia|
Phone: +61 2 9514 7777
Fax: +61 2 9514 7711
Web page: http://www.qfrc.uts.edu.au/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, September.
- Fang, Fang & Oosterlee, Kees, 2008.
"A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions,"
9319, University Library of Munich, Germany.
- Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 7700, University Library of Munich, Germany.
- Peter Carr & Jian Sun, 2007. "A new approach for option pricing under stochastic volatility," Review of Derivatives Research, Springer, vol. 10(2), pages 87-150, May.
- Peter Carr & Hélyette Geman & Dilip Madan & Marc Yor, 2005. "Pricing options on realized variance," Finance and Stochastics, Springer, vol. 9(4), pages 453-475, October.
- Alexey Medvedev & Olivier Scaillet, . "Approximation and Calibration of Short-Term Implied Volatilities under Jump-Diffusion Stochastic Volatility," Swiss Finance Institute Research Paper Series 06-08, Swiss Finance Institute, revised Jan 2006.
- Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
- Hans Buehler, 2006. "Consistent Variance Curve Models," Finance and Stochastics, Springer, vol. 10(2), pages 178-203, April.
- Andrey Itkin & Peter Carr, 2010. "Pricing swaps and options on quadratic variation under stochastic time change models—discrete observations case," Review of Derivatives Research, Springer, vol. 13(2), pages 141-176, July.
- Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:306. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Duncan Ford)
If references are entirely missing, you can add them using this form.