开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

xyrg+ · 2023年02月14日

为什么不能这么算?记得老师上课讲的是这样的

NO.PZ2020011303000190

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%.

题目问:6个月和1年的T-bill的价格是97931.5年和2年的T-bondcoupon rate6% per year价格是98.597.5,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spot rate(半年付息一次)= 2 x (100/971) = 6.186%

2. 1年的spot rate(半年付息一次)= 2 × [ (100/93)1/21 ] = 7.390%

3. T-bond是附息债券,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0.93

1.5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discount factor= 92.8/103 = 0.900971

discount factor=1/(1+r)^n

即可反求出1.5年的spot rate(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 = 89.0971

2年的discount factor= 89.0971/103 = 0.8650

discount factor=1/(1+r)^n

即可反求出2年的spot rate(半年付息一次) =7.383%.




1 个答案

pzqa27 · 2023年02月14日

嗨,爱思考的PZer你好:


两个地方不对,第一,Tbill是0息债券,这里不应该出现现金流

第二,题目告诉我们coupons at the rate of 6% per year并且semi-annual compounding.,也就是每一期的coupon应该是3,不应该是6

解决完上述问题后,您的结果应该是和答案一样的


----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

  • 1

    回答
  • 0

    关注
  • 340

    浏览
相关问题

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

2024-04-13 15:00 1 · 回答

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%. 这么做错的原因在哪里?

2023-07-13 16:30 2 · 回答

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%. 这个题答案为什么还要乘以2

2023-04-17 12:48 1 · 回答

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%. 这个题没看懂。。。。

2023-04-17 12:42 1 · 回答

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%. 理解Tbill是零息债,为何折现要考虑付息呢?又有点糊涂了。谢谢

2023-03-19 10:59 1 · 回答