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临江仙 · 2023年09月03日

如果用画图法,如何求coupon折现的pvc

NO.PZ2023020101000011

问题如下:

They move to valuation of a bond futures contract employed by Sheroda. Parisi provides Curry with the following information for a Treasury bond and calculates the price of a futures contract on this bond. The bond has a face value of $100,000, pays a 7% semiannual coupon, and matures in 15 years. The bond is priced at $156,000, has no accrued interest, and yields 2.5%. The futures contract expires in 8 months, and the annualized risk-free rate is 1.5%. There are multiple deliverable bonds, and the conversion factor for this bond is 1.098.

Based on the information provided by Parisi, which of the following correctly calculates the futures price of the Treasury bond

选项:

A.

f 0 ( T )= [ $156,000 ( 1.015 ) ( 8/ 12 ) −$3,508.6958 ] /1.098 =$140,298.21.

B.

f 0 ( T )= [ $156,000 ( 1.015 ) ( 8/ 12 ) 3,491.325 ]/ 1.098 =$140,314.03.

C.

f 0 ( T )=1.098[ $156,000 ( 1.015 ) ( 8/ 12 ) $3,508.6958 ]=$169,144.08.

解释:

The futures price is calculated as follows:

f 0 ( T )= 1 /CF( T ) { FV[ B 0 ( T+Y )+A I 0 ]A I T FVC I 0,T }

There is no accrued interest, but the bond pays a $3,500 coupon in 6 months, so the future value of the coupon at expiration will be $3,508.6958 = 3500(1.015)(2/12).

f 0 ( T )= [ $156,000 ( 1.015 ) ( 8/ 12 ) $3,508.6958 ] /1.098 =$140,298.21.

coupon折现到Now,用哪个折现率?是rf还是yield?

1 个答案
已采纳答案

李坏_品职助教 · 2023年09月03日

嗨,努力学习的PZer你好:


题目求得是future price,所以折现都是用risk-free rate 1.5%。


这个题目不建议用画图,债券期货可以直接套用公式计算:

先求出F(T)=S0×(1+rf)^T - AI_T - FVC,

再用F(T) / CF即可得到最后的Quoted Future price。

----------------------------------------------
努力的时光都是限量版,加油!

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