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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

  1. CFA II
  2. Derivative

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

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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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