Projection of Long-term Interest Rates with Maps

Abstract

There are many models for pricing financial assets. Their goals are usually to reproduce the price of quoted financial assets, e.g. the prices of bonds or to make projections and thus provide evaluations of the risk exposure of assets portfolios. A risk-management policy can be chosen and hedging ratios decided using models. More than the theoretical evaluation of financial assets, determining the hedging ratios is often the essential goal of those models. Two main approaches exist for modeling the interest rates structure and its dynamics: a parametric approach and a non-parametric one. The non-parametric approach developed in this chapter does not assume a priori hypotheses on the functional form of the process generating the interest rates structure and on the form of the distribution that characterizes the dynamic of the random variables observed. Using a historical data set, Eric de Bodt, Philippe Grégoire and Marie Cottrell use the SOM algorithm to approximate both the distribution of the interest rates structure and its deformations over time (the shocks on the interest rates structures). On this basis, a Monte-Carlo simulation gives long-term interest rates structure evolution on a 5-year horizon.