Dr. Antoine Jacquier (Imperial College London)

Title: Martingale Information Of The Implied Volatility Smile

Abstract: Given an implied volatility smile at some fi xed maturity, we wish to answer the following questions regarding the underlying stock price process: Is it a true martingale? Does it have a strictly positive mass at zero? We shall see that the answers to these two questions can be quantified precisely. In doing so, we shall revisit some of the model-free asymptotic behaviours of the implied volatility smile developed by Roger Lee and Shalom Benaim and Peter Friz. These results also give a simple characterisation of bubbles from the observation of the smile.

This talk is based on joint works with Stefano de Marco and Caroline Hillairet, and Martin Keller-Ressel