Please answer both parts a and b. I'll upvote if both parts are answered!

Digitals. As seen in the proof of BSM, for a call N(d2) = P[A(te)/F > K/F] = P[A(te) > K] i.e., N(d2) is the probability that the call option finishes in the money, see 5.30. (a) With A(0) = 100,0 = 10%, te = 1/2, r = 5%, compute the value of the following 6-month expiry digital payoff: $1,000,000 if Ate) > 100 and 0 otherwise. (b) Using same values as above, compute the value of a 6-month ex- piry knock-in call with payoff max(0, A(te) 100), but only if Ate) > 110 (See last payoff in Figure 5.9). Straddle Strangle Collar Spread Ratio Fly x2 x2 Digital Knock-in Figure 5.9: European style option payoffs Digitals. As seen in the proof of BSM, for a call N(d2) = P[A(te)/F > K/F] = P[A(te) > K] i.e., N(d2) is the probability that the call option finishes in the money, see 5.30. (a) With A(0) = 100,0 = 10%, te = 1/2, r = 5%, compute the value of the following 6-month expiry digital payoff: $1,000,000 if Ate) > 100 and 0 otherwise. (b) Using same values as above, compute the value of a 6-month ex- piry knock-in call with payoff max(0, A(te) 100), but only if Ate) > 110 (See last payoff in Figure 5.9). Straddle Strangle Collar Spread Ratio Fly x2 x2 Digital Knock-in Figure 5.9: European style option payoffs