Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model
AbstractThe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1203.5903.
Date of creation: Mar 2012
Date of revision: Aug 2012
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Web page: http://arxiv.org/
Other versions of this item:
- Jan Baldeaux & Alexander Badran, 2012. "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Research Paper Series 306, Quantitative Finance Research Centre, University of Technology, Sydney.
- 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-2012-04-03 (All new papers)
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