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CR7 · 2022年06月02日

al0 al1 到底是啥

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)

al0 al1 到底是啥

1 个答案
已采纳答案

Lucky_品职助教 · 2022年06月04日

嗨,爱思考的PZer你好:


Accrued interest是指距离上一次coupon发放日到settlement date期间应得的利息。因此AI0就是上一次coupon发放到0时刻应得的利息;AI1是上一次coupon发放到1时刻应得的利息。

可以把AI理解为怀孕的母猪肚子里小猪的价值,买卖母猪的时候,要考虑到小猪的价值,如果小猪出生了(付coupon),就需要减掉小猪的价值,没出生就要一直带着,但会随着时间增加价值

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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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