Friday, October 23, 2015

interest rates - Why isn't the Nelson-Siegel model arbitrage-free?


Assume Xt is a multivariate Ornstein-Uhlenbeck process, i.e. dXt=σdBtAXtdt

and the spot interest rate evolves by the following equation: rt=a+bXt.
After solving for Xt using etAXt and Ito and looking at T0rsds, it turns out that T0rsdsN(aT+bT(IeTA)A1X0,bTVTb)
where Vt is the covariance matrix of T0(Ie(Tu)A)A1σdBu.


This gives us the yield curve y(t)=a+bT(IetA)A1X0t+bTVtb2t

and by plugging in A=(λ10λ) we finally arrive at y(t)=a+1eλtλtC0+eλtC1+bTVtb2t.
The formula above without bTVtb2t is known as the Nelson-Siegel yield curve model. Could somebody clarify why neglecting bTVtb2t leads to arbitrage opportunities?


So I am essentially asking the following question:


Why is the above model (with bTVtb2t) arbitrage free?




No comments:

Post a Comment

technique - How credible is wikipedia?

I understand that this question relates more to wikipedia than it does writing but... If I was going to use wikipedia for a source for a res...