Smiling twice: The Heston++ model

By Claudio Pacati, Gabriele Pompa, Roberto Renò. Journal of Banking & Finance, 2018

49 citations recorded by the source corpus.

We recommend the addition of a deterministic displacement to multi-factor affine models to calibrate and hedge SPX and VIX derivatives jointly. The proposed model, labeled Heston++, calibrates both markets with an average relative error (on quoted implied volatilities over two years of data) of 2%, and a maximum relative error of 4%, without additional computational costs with respect to traditional affine benchmarks. Hedging performance on both markets is also drastically improved. The displacement can be interpreted as a volatility push-up reflecting expectations about a (risk-neutral) lower bound on forward VIX dynamics. Our empirical results document substantial correlation between the dynamics of the displacement and the variance risk premium, and still provide strong support for the presence of both price/volatility negatively correlated co-jumps and idiosyncratic jumps in the volatility dynamics, even when the displacement is added.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/5e6b640f9e03f02659e911be30e373b8f0ffed92

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Citations in the corpus

Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options (2017, background): “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).”
The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem (2020, background): “Nevertheless, probably besides those in [8] and [31], existing models with jumps do not really achieve a satisfying accuracy for the joint calibration problem.”
Joint calibration to SPX and VIX options with signature‐based models (2023, methodology): “…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.”