开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

月乔DD · 2020年06月08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)

请问一下课堂上有一部分没有很懂，为什么bond的spot price不需要乘以conversion factor呢？为什么futures price跟spot price不是一个逻辑？谢谢

添加评论
1 个答案

xiaowan_品职助教 · 2020年06月09日

嗨，爱思考的PZer你好：


同学你好，

我们做套利的过程就是同时进行现货与期货的操作，future contract 和债券现货是一比一的关系，这里不涉及到CF，

而conversion factor应用的场景是只针对期货来说的，在期货合约内部，不同的QFP和FP之间的对应关系。


-------------------------------
加油吧，让我们一起遇见更好的自己！


  • 1

    回答

  • 0

    关注

  • 402

    浏览
相关问题

NO.PZ2019010402000001 问题如下 A trar is looking for arbitrage opportunity relating to a bonfutures baseon following information: Ÿ Quotefutures price=103 Ÿ Conversion factor=1.02 Ÿ One month remaining to expiration, no coupon ring this perioŸ Quotebonprice=108 Ÿ AI0=0.1 Ÿ AIT=0.15 Ÿ Annucompounrisk-free rate=0.2%The arbitrage profit is closest to: A.0.8965 B.2.9075 C.1.3253 B is correct.考点fixeincome 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=quotefutures pri* CF=103*1.02=105.06arbitrage 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(1+0.2%)1/12(107.968−105.06)​=2.9075求No-arbitrage futures price画图:（该题合约期间没有coupon，所以PVC=0) 能否下题目中每个条件分别代表具体什么意思?

2024-06-09 16:56 2 · 回答

NO.PZ2019010402000001 问题如下 A trar is looking for arbitrage opportunity relating to a bonfutures baseon following information: Ÿ Quotefutures price=103 Ÿ Conversion factor=1.02 Ÿ One month remaining to expiration, no coupon ring this perioŸ Quotebonprice=108 Ÿ AI0=0.1 Ÿ AIT=0.15 Ÿ Annucompounrisk-free rate=0.2%The arbitrage profit is closest to: A.0.8965 B.2.9075 C.1.3253 B is correct.考点fixeincome 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=quotefutures pri* CF=103*1.02=105.06arbitrage 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(1+0.2%)1/12(107.968−105.06)​=2.9075求No-arbitrage futures price画图:（该题合约期间没有coupon，所以PVC=0) 为什么不用自然对数折现

2024-04-22 06:58 1 · 回答

NO.PZ2019010402000001 问题如下 A trar is looking for arbitrage opportunity relating to a bonfutures baseon following information: Ÿ Quotefutures price=103 Ÿ Conversion factor=1.02 Ÿ One month remaining to expiration, no coupon ring this perioŸ Quotebonprice=108 Ÿ AI0=0.1 Ÿ AIT=0.15 Ÿ Annucompounrisk-free rate=0.2%The arbitrage profit is closest to: A.0.8965 B.2.9075 C.1.3253 B is correct.考点fixeincome 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=quotefutures pri* CF=103*1.02=105.06arbitrage 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(1+0.2%)1/12(107.968−105.06)​=2.9075求No-arbitrage futures price画图:（该题合约期间没有coupon，所以PVC=0) 我根据解析中画图法算出来FP=102.9672，和103*1.02轧差后是2.09

2023-10-16 13:15 1 · 回答

NO.PZ2019010402000001 问题如下 A trar is looking for arbitrage opportunity relating to a bonfutures baseon following information: Ÿ Quotefutures price=103 Ÿ Conversion factor=1.02 Ÿ One month remaining to expiration, no coupon ring this perioŸ Quotebonprice=108 Ÿ AI0=0.1 Ÿ AIT=0.15 Ÿ Annucompounrisk-free rate=0.2%The arbitrage profit is closest to: A.0.8965 B.2.9075 C.1.3253 B is correct.考点fixeincome 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=quotefutures pri* CF=103*1.02=105.06arbitrage 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(1+0.2%)1/12(107.968−105.06)​=2.9075求No-arbitrage futures price画图:（该题合约期间没有coupon，所以PVC=0) 如题

2023-10-16 11:43 1 · 回答

NO.PZ2019010402000001 问题如下 A trar is looking for arbitrage opportunity relating to a bonfutures baseon following information: Ÿ Quotefutures price=103 Ÿ Conversion factor=1.02 Ÿ One month remaining to expiration, no coupon ring this perioŸ Quotebonprice=108 Ÿ AI0=0.1 Ÿ AIT=0.15 Ÿ Annucompounrisk-free rate=0.2%The arbitrage profit is closest to: A.0.8965 B.2.9075 C.1.3253 B is correct.考点fixeincome 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=quotefutures pri* CF=103*1.02=105.06arbitrage 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(1+0.2%)1/12(107.968−105.06)​=2.9075求No-arbitrage futures price画图:（该题合约期间没有coupon，所以PVC=0) 请问解答中arbitrage profit为什么要折现呢？

2023-09-05 08:58 1 · 回答