Interest rate "market" models: extensions and applications to caps and swaptions.

Summary This thesis studies different extensions of the Libor and Swap interest rate market models by analyzing their performance in valuing and/or hedging caps and swaptions. In addition, we specify the implementation and calibration of the different models obtained. Furthermore, we value some quanto products. To do so, we derive the dynamics of the foreign Libor forward rate under the domestic forward measure using the spot exchange rate. This approach leads to dynamics involving different covariance matrices. Finally, we develop, within the framework of the monetary economics proposed by Lioui and Poncet (2004), a short-term nominal rate model whose dynamics follow a mixed diffusion-jump process. We also discuss the impact of introducing jumps on some financial quantities such as the inflation risk premium and real and nominal interest rates.