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fansen · 2020年03月27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，我的问题是这里求得是套利，有套利是不是就可以求Value呢，为什么李老师在Valuation of Fixed-Income Contracts开头说futures不需要求Value呢

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fansen · 2020年03月27日

或者说既然可以逐日盯市，为什么还会有套利的存在？

1 个答案
已采纳答案

xiaowan_品职助教 · 2020年03月27日

嗨，努力学习的PZer你好：


同学你好，套利存在是因为在同一个时间点存在价格差，

而futures不需要求value是因为它逐日盯市，每日收盘结算后，当日实现盈亏都会到账，价值归零，由于每个交易日都是重复这个value归零的过程，所以我们是不求futures的value的。


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


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