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Affine Structure Resolution for the Vasicek model

We begin with the equation $1+B_t(t,T)-kB(t,T) = 0 \quad(1)$ \begin{align} (1) & \iff e^{-kt}+e^{-kt}B_t(t,T)+(-k)e^{-kt}B(t,T) = 0 \\ & \iff e^{-kt}+ \frac{\partial}{\partial t}\left(e^{-kt}B(t,T)\ri …
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