Stress-Test Exercises and the Pricing of Very Long-Term Bonds.

Summary The first part of this thesis introduces a new methodology for conducting stress-testing exercises. Our approach allows to consider much richer stress scenarios than in practice, which evaluate the impact of a change in the statistical distribution of factors influencing asset prices, not only the consequences of a particular realization of these factors, and take into account the reaction of the portfolio manager to the shock. The second part of the thesis is devoted to the valuation of bonds with very long maturities (over 10 years). Modeling the volatility of very long term rates is a challenge, especially because of the constraints posed by the absence of arbitrage opportunities, and most models of interest rates in the absence of arbitrage opportunities imply a constant (infinite maturity) rate limit. The second chapter studies the compatibility of the "level" factor, whose variations have a uniform impact on all the rates modeled, especially the longest ones, with the absence of arbitrage opportunities. In the third chapter, we introduce a new class of interest rate model, without arbitrage opportunities, where the limit rate is stochastic, and we present its empirical properties on a database of US Treasury bond prices.