Author(s)

D. Bloch & J.D. Aube

Abstract

We consider the implied volatility surface to characterise agents belief of the future evolution of stock price returns. However, today’s market prices do not provide us with the right future anticipations of the stock price process. This is because the implied volatility surface is neither stationary nor Markovian. It is therefore natural to model the evolution of the implied volatility surface directly. Our goal is to model the implied volatility surface with general dynamics by relating its future evolution to an observable stochastic process and by adding noises. We choose to link the stock price process to the implied volatility which implies that the volatility surface is dynamically modified according to stock price realisations. We model the stock price process discretely and using conditional expectations we define its joint distributions. We calibrate the transitio

Keywords