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Shuangshuang · 2024年08月02日

能画个图讲讲么，感觉之前答案第三年的价格看不太明白

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2023100703000079

问题如下：

A European put option, which would be expired in two years, has a strike price of $101.00. The underlying bond has three years to maturity with 7% annual coupon. It is known that the risk-neutral probability of an downward move is 0.3 in year 1 and 0.4 in year 2. The current interest rate is 3.00% At the end of year l, the rate will either be 5.88% or 4.66%. If the rate in year 1 is 5.88%, it will either rise to 8.56% or rise to 6.34% in year 2. If the rate in year 1 is 4.66%, it will either rise to 6.34% or decrease to 4.58%. The value of the put option today is closest to:

选项：

A.1.1 B.1.32 C.1.48 D.1.99

解释：

第三年的价格 难道不是 101*（1+7%）吗

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已采纳答案

李坏_品职助教 · 2024年08月03日

嗨，努力学习的PZer你好：


不是。债券在到期日（t=3时刻）的价格应该是面值加上最后一笔coupon，也就是107。


债券价格的本质是未来现金流的折现，由于t=3已经在到期日了，未来的现金流就是100+7，债券在t=3时刻的价格是（100+7）/(1+r)^0 = 107

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努力的时光都是限量版，加油！

李坏_品职助教 · 2024年08月02日

嗨，努力学习的PZer你好：


题目说这个put option还有2年就到期了。利率二叉树如下：


基础资产是债券，债券的期限是在t=3时刻。首先从t=3时刻把债券价格折现到t=2（就是上图最右侧的三个节点）。

债券在t=3时刻的价格都是107，把107的价格折现到t=2计算如下：

  1. 右上角的节点：107 / (1+8.56%) = 98.5630, 此节点的put option value = 101-98.5630=2.437
  2. 中间的节点：107/（1+6.34%）=100.6207，此节点的put option value = 101-100.6207=0.3793
  3. 右下角的节点：107/（1+4.58%）=102.3140,此节点的put option value =0.

接下来需要把t=2时刻三个节点的put option value折现到t=1时刻：

  1. t=1时刻上面的节点：（2.437 * 0.6 + 0.3793*0.4）/（1+5.88%）=1.524，
  2. t=1时刻下面的节点：（0.3793 * 0.6 + 0*0.4）/（1+4.66%）=0.2174.

最后再把t=1时刻的put option value折现到t=0时刻：

（0.7*1.524 + 0.3*0.2174）/（1+3%）=1.099≈1.10



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Shuangshuang · 2024年08月02日

第三年的价格 难道不是 101*（1+7%）吗?

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NO.PZ2023100703000079 问题如下 A Europeput option, whiwoulexpirein two years, ha strike priof $101.00. The unrlying bonhthree years to maturity with 7% annucoupon. It is known ththe risk-neutrprobability of wnwarmove is 0.3 in ye1 an0.4 in ye2. The current interest rate is 3.00% the enof yel, the rate will either 5.88% or 4.66%. If the rate in ye1 is 5.88%, it will either rise to 8.56% or rise to 6.34% in ye2. If the rate in ye1 is 4.66%, it will either rise to 6.34% or crease to 4.58%. The value of the put option toy is closest to: A.1.1 B.1.32 C.1.48 1.99 第三年的107折回第二年这个可以理解，那第二年产生的利息7为什么不用加上

2024-09-21 22:49 1 · 回答

NO.PZ2023100703000079问题如下A Europeput option, whiwoulexpirein two years, ha strike priof $101.00. The unrlying bonhthree years to maturity with 7% annucoupon. It is known ththe risk-neutrprobability of wnwarmove is 0.3 in ye1 an0.4 in ye2. The current interest rate is 3.00% the enof yel, the rate will either 5.88% or 4.66%. If the rate in ye1 is 5.88%, it will either rise to 8.56% or rise to 6.34% in ye2. If the rate in ye1 is 4.66%, it will either rise to 6.34% or crease to 4.58%. The value of the put option toy is closest to:A.1.1B.1.32C.1.481.99感谢，想看看解析谢谢！

2024-04-11 14:17 1 · 回答