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)
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