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miao999 · 2022年02月18日

不是很懂，估值不是 float rate-fix rate 的折现吗，这道题的估值方法请问在哪里讲过

  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}

不是很懂，估值不是 float rate-fix rate 的折现吗，这道题的估值方法请问在哪里讲过

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李坏_品职助教 · 2022年02月18日

嗨，努力学习的PZer你好：


这里也是用float - fix啊，pay fixed是5%，receive要用bid ask中间价，也就是(3.8% + 3.88%) / 2 = 3.84%.


因为是一个季度付息一次，所以是要用1/4 * (3.84% - 5%) * 20000000 usd = -58000 usd


由于无风险利率是3.6%年化，每个季度就是3.6% / 4 = 0.9%. 这个swap的剩余期限是3年，一共是12个季度（每个季度都会有-58000usd的现金流），所以折现如下：-58000 / (1+0.9%) + -58000 / (1+0.9%)^2 + -58000 / (1+0.9%)^3 + ... + -58000 / (1+0.9%)^12




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