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金融民工阿聪 · 2022年02月18日

为什么QBP不用乘以CF？

  1. CFA II
  2. Derivative

NO.PZ2019010402000001

问题如下：

A trader is looking for an arbitrage opportunity relating to a bond futures based on following information:

  • Ÿ Quoted futures price=103
  • Ÿ Conversion factor=1.02
  • Ÿ One month remaining to expiration, no coupon during this period
  • Ÿ Quoted bond price=108
  • Ÿ AI0=0.1
  • Ÿ AIT=0.15
  • Ÿ Annual compounded risk-free rate=0.2%

The arbitrage profit is closest to:

选项：

A.

0.8965

B.

2.9075

C.

1.3253

解释：

B is correct.

考点：fixed-income futures定价

解析:

No-arbitrage futures price:

F0(T) =(108+0.1) (1 + 0.002)1/12-0.15=107.968

市场中的futures price=quoted futures price * CF=103*1.02=105.06

arbitrage profit应该是两个futures price之差的现值

所以arbitrage profit= (107.968−105.06)(1+0.2%)1/12=2.9075\frac{(107.968-105.06)}{{(1+0.2\%)}^{1/12}}=2.9075

求No-arbitrage futures price画图:（该题合约期间没有coupon，所以PVC=0)

为什么这里算F0T的时候，quoted bond price=108直接加上0.1就完事了，为什么不需要*CF→S0=108*1.02+0.1呢？

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1 个答案

Lucky_品职助教 · 2022年02月19日

嗨，爱思考的PZer你好：


同学可能对CF的作用有疑惑，conversion factor是对quoted future的调整，而不是对quoted bond哦

以下摘自摘自厦门大学学报（哲学社会科学版）2015年第一期《国债期货定价：基本原理与文献综述》，作者 厦门大学经济学院 陈蓉， 葛骏。

与股指期货标的资产的“唯一性”不同，国债期货最主要的特点就是其标的资产的“多样性”，满足一定要求的国债均是其标的资产，都可用于到期交割。尽管有很多现货，但期货报价只有一个，因此每份国债期货合约均引入虚拟的“标准券”，期货报价以标准券报价，同时交易所公布所有可交割券与这一标准券之间的转换因子，实现标准券与真实券价格之间的转换。

具体来说，中国 5 年期国债期货合约规定，其标准券是在期货到期月时剩余期限 5 年整、票面利率 3% 的虚拟券，而只要是在期货合约到期月首日剩余期限为 4 至 7 年的记账式附息国债均是其标的资产。每份期货合约上市交易时，中金所都会公布该合约对应的所有已发行可交割券及其相应的转换因子( Conversion Factor，以下用 CF 表示) 。例如，转换因子为 0.9812，意味着该只真实可交割券的期货净价是标准券期货净价的 0. 9812 倍。

下面是原版书中对CF的表述，同学也可以阅读一下~

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