Stochastic analysis of short-rate modeling: which approach yields a better fit to data?

Abstract

This thesis investigates the extent to which the two of the most common onefactor short-rate models are able to describe the market behavior of risk free Turkish treasuries for the post-2005 period. The investigated models are those widely used ones in the literature, which has analytical solutions, namely the Vasicek Model and the Cox-Ingersoll-Ross (CIR) Model. After building the necessary mathematical and financial structure, the thesis discusses the stochastic mechanics of interest rate modeling and in light of it, the zero-coupon bond prices in the models are solved, which are needed to numerically estimate model coeffi- cients. The success of a model depends on how close it estimates the bond price to the market price. In the empirical part, the fitting performance of these two models is compared together with the current benchmark, the Nelson-Siegel (NS) Model, via the standard model fitting statistics. The estimation results reveals two important regularities: Firstly the models yield a poor fitting performance during the financial crisis period and secondly the models' degree of fit to data deteriorates as the maturity raises. Among the alternative models, the CIR in general yields the worst fit to data despite its theoretical complexity while the simple Vasicek Model achieves a high degree of fit to data. Lastly the estimated yield curves for specific dates and the zero rates of varying maturities are provided, which are expected to guide policy makers and practitioners.