Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model
AbstractIn 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.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 306.
Date of creation: 01 Mar 2012
Date of revision:
stochastic volatility plus jumps model; 3/2 model; VIX derivatives;
Other versions of this item:
- Jan Baldeaux & Alexander Badran, 2012. "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Papers 1203.5903, arXiv.org, revised Aug 2012.
- C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G1 - Financial Economics - - General Financial Markets
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-04-17 (All new papers)
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.:
- 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.
- Fang, Fang & Oosterlee, Kees, 2008.
"A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions,"
7700, 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 9319, University Library of Munich, Germany.
- 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.
- Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, July.
- 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.
- Hans Buehler, 2006. "Consistent Variance Curve Models," Finance and Stochastics, Springer, vol. 10(2), pages 178-203, April.
- Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
- 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.
- Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "Explicit implied vols for multifactor local-stochastic vol models," Papers 1306.5447, arXiv.org, revised Mar 2014.
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