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Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model

  • Jan Baldeaux
  • Alexander Badran

The paper demonstrates that a pure-diffusion 3/2 model is able 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 modelling of equity and VIX derivatives. The pure-diffusion model, however, struggles to reproduce the smile in the implied volatilities of short-term index options. One remedy to this problem is to augment the model by introducing jumps in the index. The resulting 3/2 plus jumps model turns out to be as tractable as its pure-diffusion counterpart when it comes to pricing equity, realized variance and VIX derivatives, but accurately captures the smile in implied volatilities of short-term index options.

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File URL: http://arxiv.org/pdf/1203.5903
File Function: Latest version
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Paper provided by arXiv.org in its series Papers with number 1203.5903.

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Date of creation: Mar 2012
Date of revision: Aug 2012
Handle: RePEc:arx:papers:1203.5903
Contact details of provider: Web page: http://arxiv.org/

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  1. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
  2. 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.
  3. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
  4. 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.
  5. 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.
  6. Hans Buehler, 2006. "Consistent Variance Curve Models," Finance and Stochastics, Springer, vol. 10(2), pages 178-203, April.
  7. Peter Carr & HĂ©lyette Geman & Dilip Madan & Marc Yor, 2005. "Pricing options on realized variance," Finance and Stochastics, Springer, vol. 9(4), pages 453-475, October.
  8. 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.
  9. 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.
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