Modelling Interest Rates with One-and Two-factor Gaussian Models

Specialeforsvar ved Sebastian Jan Ystrøm

Titel: Modelling Interest Rates with One- and  Two-Factor Gaussian Models

Abstract: In this thesis two Gaussian short rate models were assessed as alternatives to the interest rate model found in Nordea's IMM model for counterparty credit risk. Both the one-factor Hull-White model and the two factor Gaussian model was presented as alternatives. The models were calibrated in two ways: A historical calibration where the model-implied term structure of zero rate volatility was calibrated to the market observed volatility structure, and a risk-neutral calibration where the models were calibrated to swaption surfaces. In the Hull-White model the swaption prices could be obtained as closed-form analytical formulas and calibration was thus straight forward. For the two-factor Gaussian model the calibration was performed using closed-form approximations to the semi-analytical swaption formula. In order to assess the models' performance, out-of-sample backtests were also performed. The backtests were performed on 7 currencies each with 12 tenors. Simulations were initialized every 7 days over a period of roughly three-and-a-half years with recalibration once a quarter. To assess the performance and take into account the different starting times, realizations were transformed into uniform space using the simulations at different horizons. Neither the one-factor Hull-White nor the two-factor Gaussian model performed satisfactory in the backtest and it was concluded that the three-factor PCA-driven model already implemented in Nordea's IMM model was superior to either alternative model.

Vejleder: Rolf Poulsen
Censor:   Elisa Nicolato, Aarhus Universitet