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恬恬爱吃香菜 · 2020年03月03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，李老师课上说过，套利必须是建立在交易成立的基础上，所以这道题目的解题逻辑是现计算无套利的FP，然后和现有市场的FP求difference，现在题目中已经求出无套利的FP，但是现有市场FP=QFP+T时刻的AI，即adjusted成total price再相减，我看题目中没有加，是我理解的不对么，求解答，感谢~~

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1 个答案

xiaowan_品职助教 · 2020年03月03日

嗨，爱思考的PZer你好：


同学你好，我们第一步求 F0(T)=S0*(1+Rf)^T-AIt-FVC，由于期间没有coupon，那么F0(T)=S0*(1+Rf)^T-AIt，这里T时刻的AI已经被减去了，所以才可以和实际成交的 quoted futures price * CF 相比较做差，再进一步向前折现得到结果。


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