Volatility modeling, model calibration

Volatility is the number one factor driving the pricing, hedging, and risk-management of derivatives. In particular, the joint modeling of underlyings and their implied volatilities is of paramount importance. Volatility modeling has a long history, from Bachelier to Black-Scholes to local volatility to stochastic volatility (SV) and stochastic local volatility, and is still a very active field of research. Recent advances take into account the fact that volatility clearly depends on the path followed by the price of the underlying (path-dependent volatility), as evidenced by market data, and that log-volatility paths themselves exhibit some roughness at the daily scale (rough volatility).

We enhance volatility models so that they capture all the important stylized facts observed in market data, both static and dynamic, and develop numerical methods to calibrate them to market data.