Affine multi-factor short-rate models in term structure modeling

Abstract. This thesis gives an overview of short-rate models in term structure modeling of interest rates. The focus is in simple preference-free models with affine term structures. The thesis also shows how these models can be extended to cover credit spreads over the risk-free interest rate. The empirical section analyzes how well these models can be applied to recent interest rate data. While short-rate models are still used, more recent market models have eclipsed them in pricing of complex derivatives. The previous literature in short-rate modeling has been mainly conducted before the financial crisis of 2007–08 and there is very little literature on comparing how well these models perform in the current market structure which features negative interest rates. The first chapters give an overview of arbitrage-free pricing methodology of contingent claims and short-rate modeling of interest rates and credit spreads. These chapters present analytical pricing formulas for zero-coupon bonds with and without credit risk and semi-analytical pricing method for options on zero-coupon bonds in simple preference-free affine multi-factor short-rate models. The main finding of the empirical study shows that single-factor models do not fit the recent market data. For multi-factors models, the results were not conclusive. The calibration of multi-factor models is very hard multi-dimensional optimization problem with heavy computational burden. While the quality of the multi-factor model calibrations was mostly lacking, the mixed results suggest that insufficient computing power might be cause. The rationale for this conclusion was that the calibration algorithm could not replicate previous calibration results when a different starting population was used in optimization. It seems that there were not enough computational resources to guarantee that stochastic optimization algorithm was able to find optimal parameter values. Based on the findings of the empirical study, it seems that multi-factor short-rate models with affine term structure can be used in term structure modeling but with caveats. The whole discount curve from over-night rate to the maturity of 30 years seems to be too complex for these models but shorter sections worked much better and optimization and the computational burden may not be ignored in a more serious calibration attempt