Consider a consol bond, i.e. a bond which will forever pay one unit of cash at t = 1, 2, . . .. Suppose that the market yield y is constant for all maturities.

(a) Compute the price, at t = 0, of the consol.

(b) Derive a formula (in terms of an infinite series) for the duration of the consol.

(c) Use (a) and Proposition 22.11 in order to compute an analytical formula for the duration.

(d) Compute the convexity of the consol.

-1,T-=-D * p dy dy