Interest rate modelling

Sammanfattning: Many models have been developed throughout the years to describe the evolution of short term rates. One of the famous models is the Vasicek model. It was first introduced in 1977 and describes interest rates as a mean reversion process which is a specific characteristic that sets it apart from other financial assets. This model has the ability to let interest rates to be negative which was perceived as a weakness of the model before the 2008 financial crisis. However, it has become one of its strengths in the current negative rates environment set by central banks in an effort to stimulate the economy. The Cox–Ingersoll–Ross model was introduced in 1985 as a way to limit interest rates from being negative. Many complex and dynamics models were developed in the years that followed to describe the movement of short term rates. However, fewer models were interested in the long term rates. This is due to the impact macroeconomic variables have on these rates. In this thesis, we detail three approaches to the modeling of long term interest rates in the United States and Germany. The first one is based on anticipation of future short term rates, the second one looks at the effect on macroeconomic variables on these long term rates and the last one describes the evolution of the yield curve.