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blacklark · 2022年07月25日

期末或期初

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)

这里如果先把期末的QFP*CF+AIt折现到零时刻再与B0+AI0做比较可否?计算出来有一些差异

1 个答案

Lucky_品职助教 · 2022年07月26日

嗨,爱思考的PZer你好:


QFP*CF算出来的是市场上的期货价格,AIT是基础资产的,用于计算No-arbitrage futures price,这两个future price之间有套利机会,所以让计算,因此不能把AIT加到市场上的期货价格里哦,我们是要算两个FP进而算arbitrage profit 

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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