The formula for the price c of a European call futures option in terms of the futures price Fo is given in Chapter 17 as where d c=e[FoN(d)-KN(d)] In(Fo/K)+T/2 T and d = d-o and K, r, T, and are the strike price, interest rate, time to maturity, and volatility, respectively.

(a) Prove that FoN'

(d) = KN'(d).

(b) Prove that the delta of the call price with respect to the futures price is e** N(d).

(c) Prove that the vega of the call price is FoTN'(d)e.

(d) Prove the formula for the rho of a call futures option given in Section