Consider the construction of a trinomial tree for the general short rate model of form dy_t = κ(θ(t) − yt)dt + σdW_t, r_t = g (yt). The approach typically involves constructing the tree for dx_t = − KX_tdt + σdW_t, then on each node of the tree, solving for α(t), where y_t = x_t + (t) so that the prices of discount bonds are recovered. Assuming we have already built the tree for x_t, describe the procedure for finding a(t) on the tree, making use of Arrow-Debreu prices (i.e. prices Aⁿ_j of securities that pay 1 if and only if and only if x_t = xⁿ_j, where xⁿ_j  is spatial node j on the tree corresponding to time index n) which can be calculated from the tree. Note that we solve for α(t) on the tree, rather than calculate this analytically because otherwise we will not match discount bond prices due to discretisation errors. (Hull [Hul11] describes the building of the trinomial tree in much greater detail.)