为什么不用自然对数折现

NO.PZ2019010402000001

问题如下：

A trader is looking for an arbitrage opportunity relating to a bond futures based on following information:

Quoted futures price=103
Conversion factor=1.02
One month remaining to expiration, no coupon during this period
Quoted bond price=108
AI₀=0.1
AI_T=0.15
Annual compounded risk-free rate=0.2%

The arbitrage profit is closest to:

选项：

0.8965

2.9075

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= $\frac{(107.968-105.06)}{{(1+0.2\%)}^{1/12}}=2.9075$

求No-arbitrage futures price画图:（该题合约期间没有coupon，所以PVC=0)

为什么不用自然对数折现

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李坏_品职助教 · 2024年04月22日

嗨，爱思考的PZer你好：

那个不是对数，是指数。指数形式的叫做连续复利（cotinuously compounding），本题没有特别说明是连续复利。

而且题目条件给出的是“ Annual compounded risk-free rate”，这个意思是“按年复利”，也就是用离散复利的公式计算：

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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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NO.PZ2019010402000001 问题如下 A trar is looking for arbitrage opportunity relating to a bonfutures baseon following information: Quotefutures price=103 Conversion factor=1.02 One month remaining to expiration, no coupon ring this perio Quotebonprice=108 AI0=0.1 AIT=0.15 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: Quotefutures price=103 Conversion factor=1.02 One month remaining to expiration, no coupon ring this perio Quotebonprice=108 AI0=0.1 AIT=0.15 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

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: Quotefutures price=103 Conversion factor=1.02 One month remaining to expiration, no coupon ring this perio Quotebonprice=108 AI0=0.1 AIT=0.15 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

为什么不用自然对数折现

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