Browsing by Author "Sauli, Joose Mikko Juhani"

The study addresses an estimation problem faced by a large borrower, such as a government, related to an interest rate risk measure known as Cost-at-Risk, or CaR. The term denotes a threshold level of debt costs such that the actual debt costs incurred in a given time (say, one year) will be less than this threshold level with a given probability (say, 95 %). The main obstacle to determining CaR is that the probability distribution of future levels of interest rates is unknown. For this purpose, various models of the term structure of interest rates have been developed. This study takes one particular term structure model, the Longstaff–Schwartz model, under examination in order to determine its inherent suitability for the estimation of CaR. The model is an affine two-factor equilibrium model with analytic solutions for bond and option prices. The accuracy of the model is studied by simulating interest rate pseudo-data using a simulation program which corresponds exactly to the model’s assumptions, and then recalibrating the model to the pseudo-data. Given that the properties of the data-generating process (DGP) are known exactly, this approach allows us to compare the CaR estimates implied by the recalibrated model against the CaR implied by the actual properties of the DGP. Particular attention is paid to the methods by which the model is calibrated to data. In an effort to improve the accuracy of the Longstaff–Schwartz model, a new calibration method is developed. In order to appraise the accuracy of the Longstaff–Schwartz model, we compare its performance to that of a simpler benchmark model based on the Nelson–Siegel decomposition of the yield curve. The accuracy of the CaR estimates given by the two models is compared both in an environment where the DGP is of the Longstaff–Schwartz type, and in another environment where the DGP is of the Nelson–Siegel type. The results of the comparison can be summarized as follows. The new calibration method for the Longstaff–Schwartz model is highly accurate when the DGP is of the LS type, but is useless in the NS-type environment. When the LS model is calibrated using the technique proposed by Longstaff and Schwartz themselves, it turns out that the model gets no advantage from being correctly specified. When correctly specified, it fails to calibrate to data in about 25% of all cases, but when it is misspecified, the failure rate drops to 2.4%, and its accuracy improves and surpasses that of the NS model. These results are highly unexpected. It is possible that they are specific to the parameter values used in the simulations, but this issue is left for further research.