The Heston model is one of the most popular stochastic volatility models for Equity and FX modelling. Although it was developed more than fifteen years ago, its understanding is still not complete and many recent publications have addressed deep theoretical and implementation issues. We review...

We extend Gatheral and Jacquier SSVI volatility surface parameterisation by making the correlation maturity-dependent, obtaining necessary and su cient conditions for no calendar-spread arbitrage. Parametric families for the correlation are provided for which those conditions are explicit. This...

In this article we propose a generalisation of the recent work of Gatheral-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...

We work in the Uncertain Volatility Model setting of Avellaneda, Levy, Paras [1] and Lyons [10] (cf. also [11]). We first look at European options in a market with no interest rate and focus on theextreme case where the volatility has a lower bound but no upper bound. We show that the smallest...

We develop a dynamic version of the SSVI parameterisation for the total implied variance, ensuring that European vanilla option prices are martingales, hence preventing the occurrence of arbitrage, both static and dynamic. Insisting on the constraint that the total implied variance needs to be...