BFS 2002

Contributed Talk

A new approach to modelling and pricing derivative securities based on many assets will be presented. The ultimate, practical aim is to properly price such derivatives when the underlyings show a volatility smile/skew. Our theory allows to sample from an entirely new type of dynamics, fully compatible with earlier theory that consistently accounts for the observed volatility surfaces for a range of securities.
Within a local volatility framework we write in an analytic fashion the joint dynamics of the underlying securities affecting the derivative prices. A general treatment of a mixture of lognormals dynamical model in a multifactor setting will be presented, along with an operative proposal for the use of this model to deduce skews on baskets of many stocks. A natural extension to the case of the Libor Market Model would allow to compute quasianalytically the swap rates' smile given the smiles in the individual caplets.