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Shawnxz · 2020年12月04日

问一道题：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:

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

$c^-=\frac{0.5\times0.003378+0}{1+1.7632\%}=0.001660$

T=0：

${\text{c}}_0=\frac{0.003503\times0.5+0.001660\times0.5}{1+2.0689\%}=0.002529$

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。

因为这是欧式期权，所以只要比较最后一期对吗？

如果是美式期权，T=1时候，1.7632%也取不到对吗？

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xiaowan_品职助教 · 2020年12月04日

嗨，努力学习的PZer你好：

同学你好，

美式call只有在期间有dividend的情况下才有可能提前行权，理论上来说不分红的美式call不会提前行权，和欧式的讨论是一样的。

-------------------------------
就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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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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