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Cielling · 2020年08月18日

问一道题：NO.PZ2019010402000001 [ CFA II ]

  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)

请问为什么再算arbitrage profit时，不是用(QFP*CF+AIT)-(B0+AI0)(1+Rf)^1/12 再贴现到0时刻呢。答案没有涉及到AI
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1 个答案

WallE_品职答疑助手 · 2020年08月18日

同学你好，

您看看这个思路

我们先计算出这个国债期货的无套利情况下的FP，相当于是(S0+AI0-PVC0)×（1+r）T=FP+AIT，然后把数字带进去算出FP

然后再和市场上该国债期货对应的FP比较，如果二者不相等，就可以套利

市场上该国债期货对应的FP就是quoted futures price 再乘以 conversion factor。

套利利润就是公允的FP-QFP×CF

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