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王楚溪 · 2020年08月09日

还是不太能理解tbill那里的计算方法,请老师解释一下

问题如下:

The cash prices of 6-month and one-year Treasury bills are 97.0 and 93.0. A 1.5-year and two-year Treasury bond with coupons at the rate of 6% per year sell for 98.5 and 97.5. Calculate the six-month, 12-month, 18-month, and 24-month spot rates with semi-annual compounding.

选项:

解释:

1. The six-month rate (semi-annually compounded) is 2 x (100/971) = 0.06186 or 6.186%.

2. The one-year rate (semi-annuallycompounded) is 2 × [ (100/93)1/21 ] = 0.07390 or 7.390%.

3. The coupons on the 1.5 year bond have a value of 0.97 × 3 + 0.93 × 3 = 5.7.

The value of the final payment is therefore 98.5 − 5.7 = 92.8.

The discount factor for 1.5 years is 92.8/103 = 0.900971.

This corresponds to a spot rate (semi-annually compounded) of 7.074%.

4. The coupons on the two-year bond have a value of 3 × 0.97 + 3 × 0.93 + 3 × 0.900971 = 8.4029

The value of the final payment is therefore 97.5 8.4029 = 89.0971.

The discount factor for two years is 89.0971/103 = 0.8650.

This corresponds to a spot rate (semi-annually compounded) of 7.383%.

老师你好,请问为什么t=0.5时不能用100/(1+r)^0.5=97来推算0.5年对应的spot rate? 还是不太能分清什么时候是(1+r)^0.5什么时候是(1+r/2)^1,课上何老师讲完还是不太能记得住,麻烦老师讲解一下。谢谢!

1 个答案

品职答疑小助手雍 · 2020年08月10日

嗨,努力学习的PZer你好:


r代表年利率的话。

只有在按整年复利的时候才会用到(1+r)^0.5

半年复利的时候都是(1+r/2)^1。


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NO.PZ2020011303000190问题如下 The cash prices of 6-month anone-yeTreasury bills are 97.0 an93.0. A 1.5-yeantwo-yeTreasury bonwith coupons the rate of 6% per yesell for 98.5 an97.5. Calculate the six-month, 12-month, 18-month, an24-month spot rates with semi-annucompounng. 1. The six-month rate (semi-annually compoun is 2 x (100/97-1) = 0.06186 or 6.186%. 2. The one-yerate (semi-annuallycompoun is 2 × [ (100/93)1/2-1 ] = 0.07390 or 7.390%.3. The coupons on the 1.5 yebonhave a value of 0.97 × 3 + 0.93 × 3 = 5.7.The value of the finpayment is therefore 98.5 − 5.7 = 92.8. The scount factor for 1.5 years is 92.8/103 = 0.900971. This correspon to a spot rate (semi-annually compoun of 7.074%.4. The coupons on the two-yebonhave a value of 3 × 0.97 + 3 × 0.93 + 3 × 0.900971 = 8.4029The value of the finpayment is therefore 97.5 – 8.4029 = 89.0971. The scountfactor for two years is 89.0971/103 = 0.8650. This correspon to a spot rate(semi-annually compoun of 7.383%. 题目问6个月和1年的T-bill的价格是97和93,1.5年和2年的T-boncoupon rate是6%per year价格是98.5和97.5,计算6个月、12个月、18个月、24个月的半年付息一次的spot rate是多少?1. 6个月的spotrate(半年付息一次)= 2 x (100/97-1)= 6.186%2. 1年的spotrate(半年付息一次)= 2 × [ (100/93)1/2-1 ] = 7.390%3. T-bon附息债券,T-bill是零息的,T-bill求出来的价格就是折现系数,6个月的折现系数是0.97,12个月的折现系数是0.931.5年期的附息债券的coupon的价格= 0.97 × 3 + 0.93 × 3 = 5.7.最后一笔本金的价格=98.5 − 5.7 = 92.8.1.5年的scountfactor= 92.8/103 = 0.900971scount factor=1/(1+r)^n即可反求出1.5年的spotrate(半年付息一次) =7.074%.4. 2年期的附息债券的coupon价格=3 × 0.97 + 3 × 0.93 + 3 × 0.900971 =8.4029最后一笔本金的价格=97.5 – 8.4029= 89.09712年的scountfactor= 89.0971/103 = 0.8650scount factor=1/(1+r)^n即可反求出2年的spotrate(半年付息一次) =7.383%. ​一年半即期利率怎么比一年期利率要低,是不是不太对啊

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2023-03-19 10:59 1 · 回答