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

By Jan Baldeaux, Alexander Badran. 2012

66 citations recorded by the source corpus.

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.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/1a903981e8898daf30919ad81a418d8c6b1eba90

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Citations in the corpus

Regime-switching stochastic volatility model: estimation and calibration to VIX options (2017, methodology): “In Baldeaux and Badran (2014), Drimus (2012), a so-called 3/2 model is used as a candidate, allowing the volatility of volatility changes to be highly sensitive to the actual level of volatility.”
A regime-switching Heston model for VIX and S&P 500 implied volatilities (2014, unknown): “Alternative models such as the 3/2-model have emerged as possible candidates for fitting VIX implied volatility [3, 15].”
Joint calibration to SPX and VIX options with signature‐based models (2023, background): “…the SPX (or additionally also in the volatility) are necessary has lead to the following contributions, Sepp (2012); Papanicolaou and Sircar (2014); Baldeaux and Badran (2014); Kokholm and Stisen (2015); Pacati et al. (2018) and more recently Grzelak (2022) with a new perspective on randomization.”
Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options (2017, methodology): “There are a few models proposed to solve this calibration issue (see, for instance, Papanicolaou and Sircar 2013; Cont and Kokholm 2013; Baldeaux and Badran 2014; Carr and Madan 2014; Pacati et al. 2015).”