the spreadsheet is for the question number 1
A B C D E F G H I J K L M N O P Q R dividend rate og NN 1000 0 32701 116 19999112331111 112 6.29869 6.29889 8.16654 1.70450 15.1909 3.63405 93.17314 100.00000107.32707 115.1999 3 258964 15.1999 0000001 8.63144 23.63111 7.22707 000000 0.00000 3.53406 0.00000 5285 19.11421 36.81234 0.00000 100.00000 N LOON BOONOODOONO OROLOONDOOR OSS 182949000000000000000000 3.63405 23.53111 124 7.22707 15.1999 0.00000 0.00000 0000000 00000 19.11421 cocacocacoc CNNNNNNNNNN Probability Distribution 116.19099 NNNN 0.23236 037405 0.25766 0.07181 851234 75.35383 75.3636315443765 858123445384585 115.199991016891 132 689664114534 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, o = 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? A B C D E F G H I J K L M N O P Q R dividend rate og NN 1000 0 32701 116 19999112331111 112 6.29869 6.29889 8.16654 1.70450 15.1909 3.63405 93.17314 100.00000107.32707 115.1999 3 258964 15.1999 0000001 8.63144 23.63111 7.22707 000000 0.00000 3.53406 0.00000 5285 19.11421 36.81234 0.00000 100.00000 N LOON BOONOODOONO OROLOONDOOR OSS 182949000000000000000000 3.63405 23.53111 124 7.22707 15.1999 0.00000 0.00000 0000000 00000 19.11421 cocacocacoc CNNNNNNNNNN Probability Distribution 116.19099 NNNN 0.23236 037405 0.25766 0.07181 851234 75.35383 75.3636315443765 858123445384585 115.199991016891 132 689664114534 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, o = 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
