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· 2022年03月09日

请问这里的value计算的是t0时刻还是t=3时刻？

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021204000048

问题如下：

You are required to estimate the value of an overnight indexed swap that has three years left in its life and involves paying a fixed rate of 5% at the end of each quarter and receiving the rate implied by the overnight rate when it is compounded day-by-day during the quarter. The notional principal is USD 20 million. The current quote for a three-year overnight index swap is bid 3.80, ask 3.88. The risk-free rate is 3.6% for all maturities. All rates are compounded quarterly.

选项：

解释：

The swap rate is the average of 3.80 and 3.88, or 3.84%. The swap involves paying 5% when the market rate is 3.84%. The swaps value is the present value of:

0.25 X (0.0384 - 0.05) X USD 20,000,000 = -USO 58,000

on every payment date for the next three years.

Because the risk-free rate is 3.6%/4 = 0.9% per quarter, the value is

−∑i=11258,0001.009i-\sum_{i=1}^{12}\frac{58,000}{1.009^i}

发现自己对于这个value的时间点有点不太明白，所以根据（收入-支出）*NP公式计算出来的value是什么时刻呢？

谢谢老师解答~

根据这道题倒推，应该是t=3时刻，但是不太明白为啥是这个时刻而不是t0.

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1 个答案

李坏_品职助教 · 2022年03月09日

嗨，从没放弃的小努力你好：


这个value的计算是一个求和符合∑，也就是从t=1 直到t=12的所有现金流都要算进来。


这是一个还剩下3年期限的swap，季度支付的（at the end of each quarter），所以一共是还有3*4 = 12期现金流



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