Modeling the volatility smile for interest rate derivatives.

Summary The purpose of this thesis is to study a model of the dynamics of the interest rate curve for the valuation and management of derivative products. In particular, we wish to model the dynamics of prices depending on volatility. The market practice consists in using a parametric representation of the market, and in constructing the hedging portfolios by calculating the sensitivities with respect to the model parameters. As the model parameters are calibrated on a daily basis so that the model reproduces market prices, the self-financing property is not verified. Our approach is different, and consists in replacing the parameters by factors, which are assumed to be stochastic. Hedging portfolios are constructed by cancelling the price sensitivities to these factors. The portfolios thus obtained verify the self-financing property.