Term structure of interest rates: reconstruction, modeling and hedging.

Summary Our work consists of four chapters that are organized around the main issues facing financial markets with respect to interest rates. Chapter 1 is devoted to the comparison of five parametric methods of revealing the zero-coupon curve, based on the fitting of a discount function as a spline function or on the fitting of zero-coupon rates as a function of several parameters. Once this range has been reconstituted, the next step is to imagine how it will evolve over time, a subject that is at the heart of Chapter 2. We then consider the four main modelling trends, the adapted Black and Scholes universe [1973], models with explanatory state variables, "martingale" models, and general equilibrium models. In chapter 3, we explore a three-factor model with deterministic volatilities, with a view to the valuation and hedging of interest rate derivatives. Our objective is to permanently calibrate the model on the three deformation factors generally obtained by the A. C. P. Finally, chapter 4 takes a new look at the control of interest rate risk. The test of six different techniques on a bond portfolio to be hedged allows us to provide alternatives to the financial markets, which traditionally use the duration and duration-convexity procedures.