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Options are also options on options: how to smile with Black-Scholes
Claude Martini, Arianna Mingone
We observe that a European Call option with strike can be seen as a Call option with strike on a Call option with strike . Under no arbitrage assumptions, this yie…
Smiles in delta
Arianna Mingone
Fukasawa introduced in [Fukasawa, Math Financ, 2012] two necessary conditions for no butterfly arbitrage which require that the and functions of the Black-Scholes formu…
No arbitrage global parametrization for the eSSVI volatility surface
Arianna Mingone
The article describes a global and arbitrage-free parametrization of the eSSVI surfaces introduced by Hendriks and Martini in 2019. A robust calibration of such surfaces has alread…
Explicit no arbitrage domain for sub-SVIs via reparametrization
Claude Martini, Arianna Mingone
The no Butterfly arbitrage domain of Gatheral SVI 5-parameters formula for the volatility smile has been recently described. It requires in general a numerical minimization of 2 fu…
No arbitrage SVI
Claude Martini, Arianna Mingone
We fully characterize the absence of Butterfly arbitrage in the SVI formula for implied total variance proposed by Gatheral in 2004. The main ingredient is an intermediary characte…