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米妮涵 · 2021年09月29日

此题和上一小题求解为何不同

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NO.PZ201702190300000306

问题如下:

The value of the American-style put option on Beta Company shares is closest to:

选项:

A.

4.53.

B.

5.15.

C.

9.32.

解释:

A is correct.

Using the expectations approach, the risk-neutral probability of an up move is

π= [FV(1) - d]/(u - d) = (1.03 - 0.800)/(1.300 - 0.800) = 0.46.

An American-style put can be exercised early. At Time Step 1, for the up move, p+ is 0.2517 and the put is out of the money and should not be exercised early (X < S, 40 < 49.4). However, at Time Step 1, p- is 8.4350 and the put is in the money by 9.60 (X - S = 40 - 30.40). So, the put is exercised early, and the value of early exercise (9.60) replaces the value of not exercising early (8.4350) in the binomial tree. The value of the put at 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 regarding Exhibit 1.

The values in Exhibit 1 are calculated as follows.

At Time Step 2:

p++ = Max(0,X - u2S) = Max[0,40 - 1.3002(38)] = Max(0,40 - 64.22) = 0.

p-+ = Max(0,X - udS) = Max[0,40 - 1.300(0.800)(38)] = Max(0,40 - 39.52) = 0.48.

p- - = Max(0,X - d2S) = Max[0,40 - 0.8002(38)] = Max(0,40 - 24.32)= 15.68.

At 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.

At 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.

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?

1 个答案
已采纳答案

WallE_品职答疑助手 · 2021年09月30日

嗨,爱思考的PZer你好:


因为上一小题的 c-+和 c--都是0。相当于只有c++,你折现到time1的话也就是相当于单独折现c++ 因为其它项都是0. 这算是特殊情况,正常的不走就是从后往前一步一步折现。

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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?

2023-07-27 16:40 2 · 回答

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

2022-08-09 15:05 2 · 回答

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

2021-01-17 17:51 1 · 回答

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

2020-08-08 23:19 1 · 回答