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梦梦 · 2024年07月07日

关于APR和EAR

  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.

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}

老师好，您在解答别人问题时说到“虽然是over night的利率，但是题目说的是在每个季度结束支付，年利率是5%，我们默认这个5%是APR的形式。在计算每期的payment的时候，就类似于coupon rate，不用再把利率搞成EAR然后计算每期的金额。”这里的APR和EAR的全称是？分别是什么意思呢？

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品职答疑小助手雍 · 2024年07月07日

同学你好，APR就是年化的利率 Annual Percentage Rate

EAR就是对APR进行复利或者连续复利之列的处理得到的Effective Annual Rate

梦梦 · 2024年07月07日

明白了，谢谢

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NO.PZ2020021204000048 问题如下 You are requireto estimate the value of overnight inxeswthhthree years left in its life aninvolves paying a fixerate of 5% the enof eaquarter anreceiving the rate impliethe overnight rate when it is compouny-by-y ring the quarter. The notionprincipis US20 million. The current quote for a three-yeovernight inx swis bi3.80, ask 3.88. The risk-free rate is 3.6% for all maturities. All rates are compounquarterly.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #453e45}span.s1 {color: #505e72}span.s2 {color: #2f496b}span.s3 {color: #6b554c}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #464047}span.s1 {color: #4869}span.s2 {color: #354667}span.s3 {color: #68554c}span.s4 {color: #383 The swrate is the average of 3.80 an3.88, or 3.84%. The swinvolves 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 US20,000,000 = -USO 58,000on every payment te 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}−∑i=112​1.009i58,000​p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #443e42}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453e46}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #433c41}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #484348}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #473f45}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #464247}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #403c41}span.s1 {color: #4b6f}span.s2 {color: #665349}span.s3 {color: #565863}span.s4 {color: #7b7b7b}span.s5 {color: #4663}span.s6 {font: 6.0px Helvetica}span.s7 {color: #7f7b7f}span.s8 {color: #62595b}span.s9 {color: #635144}span.s10 {color: #67676f} 浮动端的PV=20m，固定端的PV是用未来现金流折现，PMT=5%*20m/4, I/Y=0.9, n=12, FV=20m, 得出PV=20.973m，所以swap的价值是-0.793m？

2024-09-20 21:05 2 · 回答

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