Though it is customary to use standard Gaussian term structure models for term structure modelling, this becomes theoretically implausible in cases when nominal interest rates are near zero: Gaussian models can have arbitrarily large negative rates, whereas arbitrage considerations dictate that rates should remain positive (or very slightly negative at most). Black (1995) suggests that interest rates include an optionality which restricts them to non-negative values. This introduces a non-linearity at the zero-lower bound that makes these so-called shadow-rate models a computational challenge. This dissertation analyses the shadow-rate approximations suggested by Krippner (2013) and Priebsch (2013) for the Vasicek and ˇ arbitrage-free Nelson-Siegel (AFNS) models. We also investigate and compare the accuracy of the iterated extended Kalman filter (IEKF) with that of the unscented Kalman filter (UKF). We find that Krippner’s approach approximates interest rates within reasonable bounds for both the 1-factor Vasicek and AFNS models. Prieb- ˇ sch’s first-cumulant method is more accurate than Krippner’s method for a 1-factor Vasicek model, while Priebsch’s second-cumulant method is deemed impractical ˇ because of the computational time it takes. In a multi-factor AFNS model, only Krippner’s framework is feasible. Moreover, the IEKF outperforms the UKF in terms of filtering with no significant difference in run-time.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/31152 |
| Date | 18 February 2020 |
| Creators | Esmail, Shabbirhussein |
| Contributors | Ouwehand, Peter |
| Publisher | Faculty of Commerce, Division of Actuarial Science |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Master Thesis, Masters, MPhil |
| Format | application/pdf |
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