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jecci · 2021年11月26日

请问2时刻的利率的概率为什么不是0.25、0.5、0.25

  1. CFA II
  2. Derivative

NO.PZ2019010402000022

问题如下：

Based on the following information, the value of the European-style interest rate call option is:

Assume the notional amount of the option is $1,000,000, the exercise rate is 2.6% and the RN probability is 50%.

选项：

A.

2,368

B.

2,529

C.

3,675

解释：

B is correct.

考点：interest rate option估值

解析：

T=2:

c++ = Max(0,S++ – X) = Max[0,0.029833– 0.026] = 0.003833

c+– = Max(0,S+– – X) = Max[0,0.029378 – 0.026] = 0.003378

c– – = Max(0,S– – – X) = Max[0,0.015712 – 0.026] = 0.0

T=1:

c+=0.5×0.003833+0.5×0.0033781+2.9156%=0.003503c^+=\frac{0.5\times0.003833+0.5\times0.003378}{1+2.9156\%}=0.003503

c−=0.5×0.003378+01+1.7632%=0.001660c^-=\frac{0.5\times0.003378+0}{1+1.7632\%}=0.001660

T=0：

c0=0.003503×0.5+0.001660×0.51+2.0689%=0.002529{\text{c}}_0=\frac{0.003503\times0.5+0.001660\times0.5}{1+2.0689\%}=0.002529

因为NP=1,000,000，所以call value=0.002529×1,000,000=2,529.17

在计算interest rate option value的时候，一定要特别注意折现率的选取。

请问2时刻的利率的概率为什么不是0.25、0.5、0.25
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1 个答案

lynn_品职助教 · 2021年11月26日

嗨，从没放弃的小努力你好：


2时刻的利率的概率是0.25、0.5、0.25。只不过，这里是将2时刻的利率折到1时刻，对于1时刻的C+来说，两个概率是50%，50%，对于C-来说，两个概率也是50%，50%。

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NO.PZ2019010402000022问题如下 Baseon the following information, the value of the European-style interest rate call option is:Assume the notionamount of the option is $1,000,000, the exercise rate is 2.6% anthe RN probability is 50%.A.2,368B.2,529C.3,675B is correct.考点interest rate option估值解析T=2:c++ = Max(0,S++ – X) = Max[0,0.029833– 0.026] = 0.003833c+– = Max(0,S+– – X) = Max[0,0.029378 – 0.026] = 0.003378– = Max(0,S– – – X) = Max[0,0.015712 – 0.026] = 0.0T=1:c+=0.5×0.003833+0.5×0.0033781+2.9156%=0.003503c^+=\frac{0.5\times0.003833+0.5\times0.003378}{1+2.9156\%}=0.003503c+=1+2.9156%0.5×0.003833+0.5×0.003378​=0.003503c−=0.5×0.003378+01+1.7632%=0.001660c^-=\frac{0.5\times0.003378+0}{1+1.7632\%}=0.001660c−=1+1.7632%0.5×0.003378+0​=0.001660T=0c0=0.003503×0.5+0.001660×0.51+2.0689%=0.002529{\text{c}}_0=\frac{0.003503\times0.5+0.001660\times0.5}{1+2.0689\%}=0.002529c0​=1+2.0689%0.003503×0.5+0.001660×0.5​=0.002529因为NP=1,000,000，所以call value=0.002529×1,000,000=2,529.17在计算interest rate option value的时候，一定要特别注意折现率的选取。这题我和另外一种题型混淆了 我是假设notional为100的浮动利率债券 从T2往前折现的 结果差很远 为什么不能用那个方法呢？

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