Smile in the low moments

Skew and curvature of volatility smiles are not only difficult to estimate, but also poorly reproduced by most smile expansions. Jean-Philippe Bouchaud, Lorenzo De Leo, Vincent Vargas and Stefano Ciliberti propose an expansion that effectively captures these dynamics by interpreting its parameters as payouts of exotic options for which efficient pricing methods are readily available

Understanding the shape of volatility smiles in option markets is one of the most active fields of research in quantitative finance (Gatheral, 2006, and Fouque, Papanicolaou & Sircar, 2000). The existence of an option smile is the sign that the standard Black-Scholes model is not an adequate representation of the stochastic dynamics of financial assets. A huge variety of models have been proposed over the years to account for the non-Gaussian nature of price changes and the corresponding option