The price of a bond at time T, measured in terms of its yield, is G(y_T). Assume geometric Brownian motion for the forward bond yield, y, in a world defined by a numeraire equal to a bond maturing at time T. Suppose that the growth rate of the forward bond yield is α and its volatility σy.

(a) Use Ito's lemma to calculate the process for the forward bond price in terms of α, σy, y, and G(y).

(b) The forward bond price should follow a martingale in the world considered. Use this fact to calculate an expression for α.

(c) Show that the expression for α is, to a first approximation, consistent with equation (30.1).