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daisy0405 · 2020年08月08日

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

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问题如下:

6.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:

B 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(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
1 个答案

WallE_品职答疑助手 · 2020年08月09日

同学您好,

美式期权,就是你要在每一期都要判断会不会行权。这个0.2517应该是从第二年折到第一年的value,然后又判断一次是否行权,然后继续往前折。

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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

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2021-09-29 23:19 1 · 回答

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