We study the term structure of the implied volatility in the presence of a symmetric smile. Exploiting the result by Tehranchi (2009) that a symmetric smile generated by a continuous martingale necessarily comes from a mixture of normal distributions, we derive representation formulae for the...

In this paper we consider the optimal transport approach for computing the model-free prices of a given path-dependent contingent claim in a two periods model. More precisely, we first specialize the optimal transport plan introduced in \cite{BeiglJuil}, following the construction of...

The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the dynamics of the stock and its volatility. Within this...

In this article we propose a generalisation of the recent work of Gatheral and Jacquier on explicit arbitrage-free parameterisations of implied volatility surfaces. We also discuss extensively the notion of arbitrage freeness and Roger Lee's moment formula using the recent analysis by Roper. We...