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qygeorge05 · 2023年06月25日

Future's Price vs Full Price

  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)

老师好！答案解释中“市场中的futures price=quoted futures price * CF=103*1.02=105.06”，这里future's price是指full price还是clean price? 因为这里没有再减去AI，应该是clean price对吗？

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1 个答案

Lucky_品职助教 · 2023年06月27日

嗨，从没放弃的小努力你好：


是的~

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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