Stochastic Interest Rate Modeling

In current financial markets negative interest rates have become rather persistent, while in theory it is often common practice to discard such rates as incredible and irrelevant. However, from a risk management perspective, it is of crucial importance to financial institutions to properly account for this phenomenon in their Asset Liability Management (ALM) studies. In this paper, we develop a coherent framework on how to best incorporate negative interest rates in this type of studies through a stochastic term structure model. It turns out that, from the wide range of available stochastic interest rate models, only the Lévy Forward Price model (LFPM) of Eberlein and Özkan (2005) is appropriate for ALM purposes. This paper further describes an optimization routine for calibrating this LFPM to the market prices of interest rate caplets with different strike rates and maturities. In addition, an empirical performance analysis is made of the LFPM, where we include four deterministic volatility specifications and introduce a novel parameterization of a piecewise homogeneity restriction with both deterministic and random breakpoints. This comparative analysis indicates that the LFPM is best adopted with the Linear-Exponential Volatility (LEV) specification and that deterministic breakpoints should be included, rather than random breakpoints.