Post-Crisis Interest Rate Modelling - A Rational Approach

Specialeforsvar ved Thyge Jørgensen

Titel: Post-Crisis Interest Rate Modelling - A Rational Approach

Abstract: We introduce an extension of the multi-curve linear-rational term-structure framework suggested in Crépey et al. [2016]. In this framework, the Overnight Index Swap (OIS) zero coupon bond and the London Interbank Offered Rate (LIBOR) rates are linear-rational functions of the driving factors in the model. Furthermore, we show conditions that ensure positive LIBOR rates and LIBOR-OIS spreads. We derive a tractable semi-analytical expression for the price of vanilla European options on linear products, such as swaptions, when the driving factors are n independent Cox–Ingersoll–Ross processes (CIR-processes). This yields a model that can effectively be calibrated to market data for swaptions and easily simulated for more complex interest rate products. We calibrate this model, and the two-factor log-normal model introduced in Crépey et al. [2016], to Euromarket data on swaptions, where the models only fit some features of the volatility cube. Possible extensions, to obtain a better calibration to market data, are suggested for the linear-rational models driven by either n independent CIR-processes or two log-normals

 

 

 

Vejleder:  David G. Skovmand
Censor:   Thomas Kokholm, Aarhus Universitet