1. I am looking for a derivation of the Nelson-Siegel model
$y(m)=a+b\left( \frac{1-e^{-\lambda m}}{\lambda m}\right)+c\left( \frac{1-e^{-\lambda m}}{\lambda m} -e^{-\lambda m} \right)$
It is supposed to follow the Differential Equation
$y''(m)+uy'(m)+vy(m)=0$
However, taking the derivative of $y$ and plugging that into the Differential Equation does not work. Where can I find a mathematical derivation and the assumptions beeing made? Just saying that the term structure follows aboves process is not enough.
2. Why does the Nelson-Siegel model allow arbitrage? And how do I proof it?
Ive already looked at this post
Why isn't the Nelson-Siegel model arbitrage-free?
without finding it very helpful. The paper of Bjoerk and Christensen shows inconsistency of the NS-model with Hull-White and Ho-Lee but I do not understand why arbitrage opportunities follow from this.
Is there any mathematical proof of arbitrage opportunities within the NS model?