Question 1: Assume r > 0. Use your BlackScholes calculator spread- sheet to see what happens to an at the money call option on a non-dividend paying stock (d = 0) as the time to expiry becomes very large. Compare that to what happens to that same option if d > 0 (even very small, like 0.1%). Try the same things with an in the money, and an out of the money call option. What happens? Optional: can you (briefly! one or two sentences! using an equation?) explain why? Question 2: Sonja and Erik each buy a European call option on TFS. S = 50, K = 45, = 25%, r = 4%, d = 1%, T = 3 months. Both of them delta hedge their option. 1 month later, S = 47 and Erik rebalances his delta hedge but Sonja does not. 2 months later, S = 49 and Erik again rebalances his delta hedge and Sonja does not. When the option expires, S = 45 and both Erik and Sonja close out their positions. Construct the portfolios for each of them (just like in the lecture notes above) for times t = 3 months to expiry, 2 months, 1 month, and at expiration. In the end, who makes more/loses less money, Erik or Sonja? 10 11 01234567890-234 A B C D E F G H 1 J K L M N P Q R interest rate 0.00000 Euro Call 5.29889 dividend rate 0.00000 Euro Put 5.29889 expiry 0.50000 American Call 5.29889 h S 0.12500 100.00000 American Put 5.29889 sigma 0.20000 u d p Stock 1.07327 0.03173 0.48233 0.51767 Euro Call Strike 100.00000 15 16 17 18 19 100.00000 107.32707 115.19009 123.63111 132.68964 93.17314 100.00000 86.81234 107 32707 115.19009 93.17314 100.00000 80.88579 86.81234 75.36363 5.29869 9.15654 1.70458 15.19009 3.53406 0.00000 23.63111 7.32707 0.00000 32.68964 15.19009 0.00000 0.00000 0.00000 0.00000 20 22 American Cal Strike 100.00000 23 24 25 26 27 28 Probability 29 5.29889 9.16664 1.70458 15.19009 3.53406 0.00000 23.63111 7.32707 0.00000 32.68964 15.19099 0.00000 0.00000 0.00000 0.00000 30 1.00000 0.48233 31 0.51767 0 0 Probability Distribution 0.4 32 33 34 0.3 35 36 37 38 0.2 39 132.60964 0.05412 40 115 19009 0.23236 41 100.00000 0.37406 0.1 42 86.81234 0.26766 75.36363 0.07181 75.3638316443765 86.8123445394566 100 Stock price 115.19069101680 132.689644114534 Euro Put Strike 100.00000 5.29869 1.82948 8.53144 0.00000 0.00000 0.00000 3.53406 0.00000 0.00000 13.18766 6.82686 0.00000 19.11421 13.18766 24.63617 American Put Strike 100.00000 5.29869 1.82948 8.53144 0.00000 3.53406 0.00000 0.00000 0.00000 0.00000 13.18766 6.82666 0.00000 19.11421 13.18766 2463617