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杨甜甜 · 2020年10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)

老师，讲义P45页的例题中，1.算no arbitrage FP的时候，为什么没有减AIt？2.FP=QFP*CF算完后，还加了0.2的AIt，才算的profit，本题为什么不加呢？麻烦老师详细说下

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2 个答案

lynn_品职助教 · 2021年11月26日

嗨，从没放弃的小努力你好：


如果考题没有特殊说要dirty price，默认用clean price

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努力的时光都是限量版，加油！

xiaowan_品职助教 · 2020年10月10日

嗨，爱思考的PZer你好：


同学你好，

讲义中那道题是教材的一道课后题，它的解析写的是有歧义的，它的计算是用dirty的价格来计算的，第一步求出来无套利状态下的FP是dirty的，后面为了求profit，所以要把实际FP也变成dirty的，这样子计算结果才没有误差。

现在这道题是全部用clean的价格来算的，同学可以听一下我们课后题班case1就是这道题，老师就这个问题有很详细的讲解。


-------------------------------
努力的时光都是限量版，加油！


Carol · 2021年11月26日

我还是没懂，为什么讲义用Dirty price这里用Clean price。。那考试到底用Dirty还是用Clean

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