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赵小瓜 · 2020年03月18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)

老师您好，我想问一下，这道题目如何逃离，不是先借债券换成现金收利息，然后到期还债券，赚了个利息的差？那不就是未来才可以获利？那不是应该算未来的值？为什么要折现到现在

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1 个答案

xiaowan_品职助教 · 2020年03月18日

嗨，努力学习的PZer你好：


同学你好，这个套利的profit我们在0时刻就可以计算出来，题目中要求计算 arbitrage profit ，都是要折现到0时刻，参考例题

另外，套利的方式我们可以选择在到期日拿到这笔利润，我们也可以选择在0时刻先借这笔利润折现到0时刻的值，获得资金使用权，

等到期时，再用获得的利润去偿还我们多借出的这笔钱，相当于提前使用了利润。


-------------------------------
加油吧，让我们一起遇见更好的自己！


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