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Maxy · 2023年10月16日

请问画图法计算过程可以写一下吗？

  1. CFA II
  2. Derivative

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= (107.968−105.06)(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)

我根据解析中画图法算出来FP=102.9672，和103*1.02轧差后是2.09

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1 个答案

李坏_品职助教 · 2023年10月16日

嗨，爱思考的PZer你好：


根据解析里面的图，理论上的FP = （S0+AI0 - PVC）*(1+rf)^T - AI_T = (bond price 108+0.1)*（1+0.002）^1/12 - 0.15，需要注意的是,：

  1. 题目说了“One month remaining to expiration, no coupon during this period”，所以PVC=0；
  2. S0指的是当前债券现货价格，S0=108；
  3. 题目的AI_0和AI_T的顺序不要搞反了。


理论上的FP = 107.968, 但是此时市场实际报价是Quoted futures price * CF = 105.06，这个和理论上的FP有价差。

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