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Qqnd · 2022年09月06日

比较这道题和李老师视频中的例题

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= (107.968105.06)(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,我看了前面两个同学的提问,也不是很明白为什么用QFPxCF+AIT折现算出来的数字会稍微不同,看到了解释是说AIT的缘故,回去翻看了李老师的例题,请问这道题的条件或场景和李老师在这个视频中的第二个例题在哪些方面有不同?例题中用了QFPxCF+AIT往前折现的方法:“Fixed-Income Forward and Futures Contracts Pricing-Example“
2 个答案
已采纳答案

Lucky_品职助教 · 2022年09月07日

嗨,爱思考的PZer你好:


一样的,这道题在计算F0(T) 时就减去了AIT 0.15,例题是在算市场价格的时候加上AIT 0.2,算arbitrage profit的时候结果是一样的,都是这两个price的差值

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

𝒜𝒩𝒥𝒜 安雅🎃 · 2023年02月02日

老师好,所以是【要嘛在计算future price时,把市场future price和no-arbitrage futures price都给加上AIT,要嘛都不加AIT】,我的理解对吗?

Lucky_品职助教 · 2023年02月04日

嗨,努力学习的PZer你好:


回复𝒜𝒩𝒥𝒜 安雅:是的~

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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