no code implementations • 5 Apr 2022 • Florian Bourgey, Stefano De Marco, Peter K. Friz, Paolo Pigato
Several asymptotic results for the implied volatility generated by a rough volatility model have been obtained in recent years (notably in the small-maturity regime), providing a better understanding of the shapes of the volatility surface induced by rough volatility models, and supporting their calibration power to S&P500 option data.
no code implementations • 21 Feb 2022 • Florian Bourgey, Stefano De Marco, Emmanuel Gobet
We provide explicit approximation formulas for VIX futures and options in forward variance models, with particular emphasis on the family of so-called Bergomi models: the one-factor Bergomi model [Bergomi, Smile dynamics II, Risk, 2005], the rough Bergomi model [Bayer, Friz, and Gatheral, Pricing under rough volatility, Quantitative Finance, 16(6):887-904, 2016], and an enhanced version of the rough model that can generate realistic positive skew for VIX smiles -- introduced simultaneously by De Marco [Bachelier World Congress, 2018] and Guyon [Bachelier World Congress, 2018] on the lines of [Bergomi, Smile dynamics III, Risk, 2008], that we refer to as 'mixed rough Bergomi model'.
no code implementations • 11 May 2021 • Florian Bourgey, Stefano De Marco
We consider the pricing of VIX options in the rough Bergomi model.
no code implementations • 7 Jul 2020 • Stefano De Marco
It is well know that, in the short maturity limit, the implied volatility approaches the integral harmonic mean of the local volatility with respect to log-strike, see [Berestycki et al., Asymptotics and calibration of local volatility models, Quantitative Finance, 2, 2002].
1 code implementation • 3 May 2017 • Stefano De Marco, Caroline Hillairet, Antoine Jacquier
We study the shapes of the implied volatility when the underlying distribution has an atom at zero and analyse the impact of a mass at zero on at-the-money implied volatility and the overall level of the smile.
