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SHAO · 2024年07月02日

老师,看不懂答案,可以画图讲解一下吗

NO.PZ2023041003000017

问题如下:

Kemper’s second investment idea is to purchase a 10-year Treasury note futures contract. The underlying 2%, semi-annual 10-year Treasury note has a dirty price of 104.17. It has been 30 days since the 10-year Treasury note’s last coupon payment. The futures contract expires in 90 days. The quoted futures contract price is 129. The current annualized three-month risk-free rate is 1.65%. The conversion factor is 0.7025. Doyle asks Kemper to calculate the equilibrium quoted futures contract price based on the carry arbitrage model.

The equilibrium 10-year Treasury note quoted futures contract price is closest to:

选项:

A.

147.94.

B.

148.89.

C.

149.78.

解释:

The equilibrium 10-year quoted futures contract price based on the carry arbitrage model is calculated as


CF = 0.7025

B0 = 104.00

AI0 = 0.17

AIT = (120/180×0.02/2)*100 = 0.67

FVCI = 0


老师,看不懂答案,可以画图讲解一下吗

1 个答案

李坏_品职助教 · 2024年07月02日

嗨,努力学习的PZer你好:


这是一份债券期货合约,距离上次支付coupon已经过了30天,距离期货合约到期日还有90天。

题目最后问的是理论上的QFP是多少?

QFP(就是下面的QF0(T))公式如下:

QFP = [债券的full price * (1+无风险利率)^T - AIT - FVC] / CF。


无风险利率是1.65%,期货合约还有90天到期,所以T=90/360=1/4.

AIT指的是在期货合约到期日的accrued interest,从上一次支付coupon到期货的到期日之间,一共有120天,而债券的票面利率是2%,并且是semi-annual(半年支付一次coupon),所以AIT = 100* 2%/2 * (120/180)=0.67.


在整个期货合约存续期内,债券没有支付coupon,所以FVC = 0.

CF就是conversion factor = 0.7025.


所以QFP = [104.17*(1+0.0165)^(1/4) - 0.67 - 0] / 0.7025 = 147.94

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

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