Black-76 Formula. 6 In addition to futures, options on futures contracts are actively traded on exchanges. The expiration date te of the option need not coincide with the forward date T of the futures contract, and the payoff of a call option on a futures contract is max(0,FA(te,T)K). (a) Derive the commonly used Black's Formula for calls on futures by completing the missing steps below C(0)=erteE[max(0,FA(te,T)K)]=erteer(Tte)E[max(0,A(te)Ker(Tte))]=erte[FA(0,T)N(d1)KN(d2)] where d1,2=teln(FA(0,T)/K)21te Note that when T=te, Black's Formula reduces to BSM Formula. b) On Friday 2020 Nov-13, the SPDR S\&P 500 ETF (SPY) settled at 358.10, while S\&P 500 December futures contract, ESZ0, with final settlement date of 2020-Dec-18 (3rd Friday of quarter-end) settled at 3580, and the 3600-strike End-Of-Month (expiration date 2020-Nov30) call option on ESZ0 settled at 43.40. Using r=0.05% (5 bp's), and Act/365 for fractions of time, find the implied volatility of the call option