III. American options Consider an American put option 5 months from expiration, with spot price 50, strike price 50, a risk free rate of 10%, and volatility of 40% per annum. Base your computations on a 5-step tree. 16. What is the size of an up move: (a) 2.34; (b) 1.12; (c) 1.89; (d) 10; 17. What is the size of a down move: (a) 1.57; (b) 0.58 (c) 0.66; (d) 0.89; 18. What is the risk neutral probability of an up move: (a) 0.25; (b) 0.4; (c) 0.6; (d) 0.51 19. What is the spot price at node (5,0): (a) 22.03; (b) 28.07; (c) 14.63; (d) 29.99; 20. What is the spot price at node (5,1): (a) 35.36; (b) 39.69; (c) 44.55; (d) 50; 21. What is the spot price at node (5,4): (a) 70.7; (b) 79.35; (c) 56.12; (d) 62.99; 22. What is the spot price at node (5,5): (a) 23.56; (b) 56.12; (c) 50; (d) 89.07; 23. What is the European put price at node (5,0): (a) 21.93; (b) 31.5; (c) 35.36; (d) 39.69 24. What is the European put price at node (5,1): (a) 0; (b) 14.64; (c) 63.7; (d) 3.76; 25. What is the European put price at node (5,2): (a) 5.45; (b) 0; (c) 75; (d) 14.64; 26. What is the European put price at node (5,5): (a) 12.32; (b) 14.44; (c) 3.56; (d) 0; 27. What is the European put price at node (4,1): (a) 9.90; (b) 12.32; (c 10.57; (d) 3.43; 28. What is the American put price at node (4,1): (a) 0; (b) 4.56; (c) 7.32; (d) 10.31; 29. What is the American put price at node (4,0): (a) 20.32; (b) 14.56; (c) 18.50; d) 10.31; 30. What is the American put price at node (3,0): (a) 11.62; (b) 14.64; (c) 16.30; (d) 14.23 2 1 III. American options Consider an American put option 5 months from expiration, with spot price 50, strike price 50, a risk free rate of 10%, and volatility of 40% per annum. Base your computations on a 5-step tree. 16. What is the size of an up move: (a) 2.34; (b) 1.12; (c) 1.89; (d) 10; 17. What is the size of a down move: (a) 1.57; (b) 0.58 (c) 0.66; (d) 0.89; 18. What is the risk neutral probability of an up move: (a) 0.25; (b) 0.4; (c) 0.6; (d) 0.51 19. What is the spot price at node (5,0): (a) 22.03; (b) 28.07; (c) 14.63; (d) 29.99; 20. What is the spot price at node (5,1): (a) 35.36; (b) 39.69; (c) 44.55; (d) 50; 21. What is the spot price at node (5,4): (a) 70.7; (b) 79.35; (c) 56.12; (d) 62.99; 22. What is the spot price at node (5,5): (a) 23.56; (b) 56.12; (c) 50; (d) 89.07; 23. What is the European put price at node (5,0): (a) 21.93; (b) 31.5; (c) 35.36; (d) 39.69 24. What is the European put price at node (5,1): (a) 0; (b) 14.64; (c) 63.7; (d) 3.76; 25. What is the European put price at node (5,2): (a) 5.45; (b) 0; (c) 75; (d) 14.64; 26. What is the European put price at node (5,5): (a) 12.32; (b) 14.44; (c) 3.56; (d) 0; 27. What is the European put price at node (4,1): (a) 9.90; (b) 12.32; (c 10.57; (d) 3.43; 28. What is the American put price at node (4,1): (a) 0; (b) 4.56; (c) 7.32; (d) 10.31; 29. What is the American put price at node (4,0): (a) 20.32; (b) 14.56; (c) 18.50; d) 10.31; 30. What is the American put price at node (3,0): (a) 11.62; (b) 14.64; (c) 16.30; (d) 14.23 2 1