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月乔DD · 2020年06月08日

问一道题：NO.PZ2019010402000001

  1. CFA II
  2. Derivative

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)

请问一下课堂上有一部分没有很懂，为什么bond的spot price不需要乘以conversion factor呢？为什么futures price跟spot price不是一个逻辑？谢谢

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1 个答案

xiaowan_品职助教 · 2020年06月09日

嗨，爱思考的PZer你好：


同学你好，

我们做套利的过程就是同时进行现货与期货的操作，future contract 和债券现货是一比一的关系，这里不涉及到CF，

而conversion factor应用的场景是只针对期货来说的，在期货合约内部，不同的QFP和FP之间的对应关系。


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