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ZF Everyday · 2022年07月29日

与上个同学的问题一致

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= (107.968105.06)(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)

这里如果先把期末的QFP*CF+AIt折现到零时刻再与B0+AI0做比较可否?

请老师能否详细解答一下,就是自己会第一反应也是这个方式,可能还是有些概念不是很清晰,看了老师解答,感觉太简单了,懵圈。

4 个答案
已采纳答案

Lucky_品职助教 · 2022年07月31日

嗨,从没放弃的小努力你好:


同学你好,我们现在比较的是无套利公式算出来的future price和市场上的future price,看看两者是否相等。因为市场上的future price 的报价是不含AI的,所以我们通过无套利公式计算出来的future price 也应该是不含AI的,两者才能比较。

而我们在通过无套利公式计算future price的时候,0时刻和期末都是要加上AI,而且这里不是给F0加AI0 ,而是给S0加AI0. 这样才能考虑到所有的现金流。

总结来说,就是在计算future price的时候,我们需要加上期初和期末的AI,而在比较市场上的future price和no arbitrage future price的时候,AIt是不考虑进去的。

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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虽然现在很辛苦,但努力过的感觉真的很好,加油!

徒慕君 · 2022年09月23日

这个题0~T时间只有一个月是吗?

Lucky_品职助教 · 2022年09月25日

嗨,从没放弃的小努力你好:


回复徒慕君:是的,One month remaining to expiration


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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

Lucky_品职助教 · 2022年08月03日

嗨,爱思考的PZer你好:


同学还有什么疑问吗?市场上该国债期货对应的FP就是quoted futures price 再乘以 conversion factor,不含AIT。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

ZF Everyday · 2022年08月02日

QFP*CF算出来的是市场上的期货价格,AIT是基础资产的,用于计算No-arbitrage futures price,这两个future price之间有套利机会,所以让计算,因此不能把AIT加到市场上的期货价格里哦,我们是要算两个FP进而算arbitrage profit 

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