Une modélisation de la surface de volatilité implicite par processus à sauts

The aim of this paper is the study of the dynamics of CAC40 options implied volatility surface. Using a functional form of Principal Component Analysis, based on a Karhunen-Loève decomposition, we isolate and analyse principals shocks factors influencing the surface. Our results suggest different behaving for short and long term volatilities: short term volatilities are well represented by a two-factor model, while three factors are necessary for long term volatilities. We obtain an orthogonal base, in which we project the implied volatility surface. Studying the time series of the obtained factors, we show that these are well represented by jump processes, particularly the first factor, which represents the global variation of the implied volatility surface. Actually, our simulations indicate that adding a jump component significantly improve the prediction power of the model.