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yinyincat · 2020年03月29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，你好，

为什么求无套利的future price里要减AI (T), 而计算市场quoted future price 就只是乘以conversion factor，而不用减去AI(T)呢？我记得书中例题算无套利的future price的时候反而没有没有减去AI (T), 我的理解是因为期间没有coupon，所以AI (T)为0. 那这题也说了期间没有coupon。求无套利期货价格和算市场期货价格，什么时候要包括AI (T)，什么时候不用？

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xiaowan_品职助教 · 2020年03月29日

嗨，从没放弃的小努力你好：


同学你好，我们做这一类的题目遵循的就是我截图这页的公式

要明确债券期货的报价都是净价，不包含AI，而实际的交割价格是full price，包含AI的；

这道题说合约期间没有coupon，但是债券本身在超出这个合约时长时，可能还有coupon，只不过不在我们这道题的讨论中，所以才会出现题目中给的AI0和AIT，如果完全没有coupon，AI0应该为0，所以这道题目按照题干中所给条件带入公式即可，遵循的原理是：0时刻的full price - 期间coupon现值 = 到期时刻的full price

 


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