问一道题：NO.PZ201702190300000306 第6小题 [ CFA II ]

NO.PZ201702190300000306 问题如下 The value of the American-style put option on Beta Company shares is closest to: A.4.53. B.5.15. C.9.32. B is correct.Using the expectations approach, the risk-neutrprobability of up move isπ= [FV(1) - /(u - = (1.03 - 0.800)/(1.300 - 0.800) = 0.46.American-style put cexerciseearly. Time Step 1, for the up move, p+ is 0.2517 anthe put is out of the money anshoulnot exerciseearly (X S, 40 49.4). However, Time Step 1, p- is 8.4350 anthe put is in the money 9.60 (X - S = 40 - 30.40). So, the put is exerciseearly, anthe value of early exercise (9.60) replaces the value of not exercising early (8.4350) in the binomitree. The value of the put Time Step 0 is nowp = PV[πp+ + (1 - π)p-] = [1/(1.03)][0.46(0.2517) + 0.54(8.4350)] = 4.54.Following is a supplementary note regarng Exhibit 1.The values in Exhibit 1 are calculatefollows.Time Step 2:p++ = Max(0,X - u2S) = Max[0,40 - 1.3002(38)] = Max(0,40 - 64.22) = 0. p-+ = Max(0,X - u) = Max[0,40 - 1.300(0.800)(38)] = Max(0,40 - 39.52) = 0.48.p- - = Max(0,X - S) = Max[0,40 - 0.8002(38)] = Max(0,40 - 24.32)= 15.68.Time Step 1:p+ = PV[πp++ + (1 - π)p-+] = [1/(1.03)][0.46(0) + 0.54(0.48)] = 0.2517. p- = PV[πp-+ + (1 - π)p- -] = [1/(1.03)][0.46(0.48) + 0.54(15.68)]=8.4350.Time Step 0:p = PV[πp+ + (1 - π)p-] = [1/(1.03)][0.46(0.2517) + 0.54(9.6)] = 5.1454.中文解析本题考察的是计算美式看跌期权的价值，需要注意的是在t=1的节点，需要判断是否有必要提前行权。在本题中，在p- 的确定时，就需要考虑这个问题，如果在t=1时刻立即行权，p- 等于9.6，如果在t=2时刻行权，折现后求得的p- 为8.4350.两者取大，因此应该在t=1时刻行权，得到p- 等于9.6.然后再根据p- =9.6，p+ =0.2517折现到0时刻得到p0. P+和P-为什么不统一呢，就是折现就都折现，不折现就都不折现，怎么有的折现有的是直接算的？

NO.PZ201702190300000306 问题如下 The value of the American-style put option on Beta Company shares is closest to: A.4.53. B.5.15. C.9.32. B is correct.Using the expectations approach, the risk-neutrprobability of up move isπ= [FV(1) - /(u - = (1.03 - 0.800)/(1.300 - 0.800) = 0.46.American-style put cexerciseearly. Time Step 1, for the up move, p+ is 0.2517 anthe put is out of the money anshoulnot exerciseearly (X S, 40 49.4). However, Time Step 1, p- is 8.4350 anthe put is in the money 9.60 (X - S = 40 - 30.40). So, the put is exerciseearly, anthe value of early exercise (9.60) replaces the value of not exercising early (8.4350) in the binomitree. The value of the put Time Step 0 is nowp = PV[πp+ + (1 - π)p-] = [1/(1.03)][0.46(0.2517) + 0.54(8.4350)] = 4.54.Following is a supplementary note regarng Exhibit 1.The values in Exhibit 1 are calculatefollows.Time Step 2:p++ = Max(0,X - u2S) = Max[0,40 - 1.3002(38)] = Max(0,40 - 64.22) = 0. p-+ = Max(0,X - u) = Max[0,40 - 1.300(0.800)(38)] = Max(0,40 - 39.52) = 0.48.p- - = Max(0,X - S) = Max[0,40 - 0.8002(38)] = Max(0,40 - 24.32)= 15.68.Time Step 1:p+ = PV[πp++ + (1 - π)p-+] = [1/(1.03)][0.46(0) + 0.54(0.48)] = 0.2517. p- = PV[πp-+ + (1 - π)p- -] = [1/(1.03)][0.46(0.48) + 0.54(15.68)]=8.4350.Time Step 0:p = PV[πp+ + (1 - π)p-] = [1/(1.03)][0.46(0.2517) + 0.54(9.6)] = 5.1454.中文解析本题考察的是计算美式看跌期权的价值，需要注意的是在t=1的节点，需要判断是否有必要提前行权。在本题中，在p- 的确定时，就需要考虑这个问题，如果在t=1时刻立即行权，p- 等于9.6，如果在t=2时刻行权，折现后求得的p- 为8.4350.两者取大，因此应该在t=1时刻行权，得到p- 等于9.6.然后再根据p- =9.6，p+ =0.2517折现到0时刻得到p0. 如题

NO.PZ201702190300000306 上一小题是求欧式看涨期权的价值，就是直接得到time 2的C++,C+-和C--，然后就直接用rf往前折现两年变得出价值 这题为什么是先折现到time 1，然后再这些到0时刻？

5.15. 9.32. B is correct. Using the expectations approach, the risk-neutrprobability of up move is π= [FV(1) - /(u - = (1.03 - 0.800)/(1.300 - 0.800) = 0.46. American-style put cexerciseearly. Time Step 1, for the up move, p+ is 0.2517 anthe put is out of the money anshoulnot exerciseearly (X 40，p1+=0

5.15. 9.32. B is correct. Using the expectations approach, the risk-neutrprobability of up move is π= [FV(1) - /(u - = (1.03 - 0.800)/(1.300 - 0.800) = 0.46. American-style put cexerciseearly. Time Step 1, for the up move, p+ is 0.2517 anthe put is out of the money anshoulnot exerciseearly (X < S, 40 < 49.4). However, Time Step 1, p- is 8.4350 anthe put is in the money 9.60 (X - S = 40 - 30.40). So, the put is exerciseearly, anthe value of early exercise (9.60) replaces the value of not exercising early (8.4350) in the binomitree. The value of the put Time Step 0 is now p = PV[πp+ + (1 - π)p-] = [1/(1.03)][0.46(0.2517) + 0.54(9.60)] = 5.1454. Following is a supplementary note regarng Exhibit 1. The values in Exhibit 1 are calculatefollows. Time Step 2: p++ = Max(0,X - u2S) = Max[0,40 - 1.3002(38)] = Max(0,40 - 64.22) = 0. p-+ = Max(0,X - u) = Max[0,40 - 1.300(0.800)(38)] = Max(0,40 - 39.52) = 0.48. p- - = Max(0,X - S) = Max[0,40 - 0.8002(38)] = Max(0,40 - 24.32)= 15.68. Time Step 1: p+ = PV[πp++ + (1 - π)p-+] = [1/(1.03)][0.46(0) + 0.54(0.48)] = 0.2517. p- = PV[πp-+ + (1 - π)p- -] = [1/(1.03)][0.46(0.48) + 0.54(15.68)]=8.4350. Time Step 0: p = PV[πp+ + (1 - π)p-] = [1/(1.03)][0.46(0.2517) + 0.54(8.4350)] = 4.5346.请问既然已经确定在1时刻行权了，为什么在计算put value时还要加上0。2517呢，这个地方不太明白