We propose a non-linear model of filtering in discrete time. The signal is linear but noises are multiplicative and non-Gaussian. We exhibit a class of distributions including the standard centered Gaussian which is closed for the filtering algorithm.

We propose new closed-form pricing formulas for interest rate options which guarantee perfect compatibility with volatility smiles. These cap pricing formulas are computed under variance optimal measures in the framework of the market model or the Gaussian model and achieve an exact calibration...

This paper constructs a model for the evolution of a risky security that is consistent with a set of observed call option price. It explicitly treats the fact that only a discrete data set can be observed in practice, The framework is general and allows for state dependent volatility and jumps.

We consider the mean-variance hedging problem when asset prices follow ItÆ processes in an incomplete market framework. The hedging numÊraire and the variance-optimal martingale measure appear to be a key tool for characterizing the optimal hedging strategy (see GouriÊroux et al. 1996;...

We consider the mean-variance hedging problem when the risky assets price process is a continuous semimartingale. The usual approach deals with self-financed portfolios with respect to the primitive assets family. By adding a numéraire as an asset to trade in, we show how self-financed...