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

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  • Jan Baldeaux
  • Alexander Badran

Abstract

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. The pronounced implied volatility smile produces artificially inflated fitted parameters, resulting in unrealistically high VIX option implied volatilities. To remedy these shortcomings, jumps are introduced. The resulting model is able to better fit short-term index option implied volatilities while producing more realistic VIX option implied volatilities, without a loss in tractability.

Suggested Citation

  • Jan Baldeaux & Alexander Badran, 2014. "Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(4), pages 299-312, September.
    • Handle: RePEc:taf:apmtfi:v:21:y:2014:i:4:p:299-312
    DOI: 10.1080/1350486X.2013.868631
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • 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

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