Kalman Filtering and the Estimation of Multi-factor Affine Term Structure Models - Tokwe,Thabo (African Institute of Financial Markets and Risk Management, 2019)
When optimising the likelihood function one often encounters various stationary points and sometimes discontinuities in the parameter space (Gupta and Mehra, 1974). This is certainly true for a majority of multi-factor affine term structure models. Practitioners often recover different parameter optimisations depending on the initial parameters. If these parameters result in different option prices, the implications would be severe. This paper examines these implications through numerical experiments on the three-factor Vasicek and Arbitrage-free Nelson-Siegel (AFNS) models. The numerical experiments involve Kalman filtering as well as likelihood optimisation for parameter estimation. It was found that the parameter sets lead to the same short rate process and thus the same model. Moreover, likelihood optimisation in the AFNS does not result in different parameter sets irrespective of the starting point.