BFS 2002

Contributed Talk

Implied Volatility Smiles

Jérôme Busca, Henri Berestycki, Rama Cont, Igor Florent

A number of models have been proposed in order to account for observed implied volatility smiles. Popular solutions include local volatility, stochastic volatility, jumps in the underlying and/or in the volatility, and combinations of those. In practice one is faced with two basic issues: i) how to compute effectively and accurately the implied volatility surface that each model generates? ii) how to choose between those models and how to calibrate their parameters on market data? It is the purpose of the talk to address these topics. An essential idea is that all the models exhibit very different qualitative behaviours. In particular several asymptotic regimes will be given, in an attempt to classify those models. One can then take advantage of the asymptotics to propose well-posed calibration procedures in some cases. This talk is based on recent joint works with H. Berestycki (EHESS, Paris), R. Cont (Ecole Polytechnique, Paris) and I. Florent (CCF, HSBC Group, Paris).