Implementation of a New Concept of Duration with respect to the Stochastic Fluctuations of the Yield Surface

Abstract

One objective of this Master thesis is to give an overview and discussion of the most important stochastic models for the dynamics of the yield surface. Since interest rates are of stochastic nature, and e.g. insurance companies are obligated to set aside reserves for future payments, exposure to interest rate risk is inevitable. The management of interest rate risk of future financial obligations is an important aspect of handling any financial institution, and during the thesis we will be introduced to some methods which are currently used in the industry. However future liabilities are often of complex nature, and the most recognized methods of measuring this sensitivity fail, because they rely on assumptions which are unrealistic. The main result of this thesis, and my contribution to this field of research, is the construction of a consistent calibration for a first order approximation of stochastic duration. This objective has indeed proved challenging, as earlier attempts have only lead to problems with minimization criteria failing to converge, and/or calibration algorithms which resulted in coefficients that were not unique for the given constraints and empirical data. This new concept of stochastic duration is likely to serve as an important tool of risk management due to fewer assumptions to both the yield surface dynamics and of the portfolios to which we measure duration. The main obstacle at this point is however the difficulty of constructing satisfactory calibration methods.