Slope of the short end

The slope of the money market curve can be equated to the slope of the zero curve for $t\to 0$, i.e. $\lim_{t\to 0}\partial y(t)/\partial t$. Since

$$\frac{e^{tD}-1}{t} = D + {1\over 2}\,t\,D^2 + o(t^2)$$ (12)

the short-end slope is

$$\lim_{t\to 0}\frac{\partial y(t)}{\partial t} = \lim_{t\... ...^-\,Q\,e_1 = {1\over 2}\,\xi^\prime\,{A^\star}^\prime\,e_1$$ (13)