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YAO Monica · 2022年04月18日

期利率转化成即期价格的原理是什么？

  1. CFA II
  2. Fixed Income

NO.PZ2016022702000009

问题如下：

The one-year spot rate r(1) = 5% and the forward price for a one-year zero-coupon bond beginning in one year is 0.9346. The spot price of a two-year zero-coupon bond is closest to:

选项：

A.

0.87.

B.

0.89.

C.

0.93.

解释：

B is correct.

We can convert spot rates to spot prices and use the forward pricing model, so have P(1)= 1(1.05)1=0.9524\frac1{{(1.05)}^1}=0.9524

The forward pricing model is P(T*+T)=P(T*)F(T*,T),

so P(2)=P(1)F(1,1)= 0.9524 × 0.9346 = 0.8901

考点：forward pricing model

我们可以将即期利率转化成即期价格P(1)=1/(1.05)=0.9524。再通过forward pricing model，P(T*+T)=P(T*)F(T*,T)，得到P(2)=P(1)×F(1,1)=0.9524×0.9346=0.8901。

请问期利率转化成即期价格的原理是什么？假设面值=1，求t=0时刻price，是这么理解吗？

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已采纳答案

pzqa015 · 2022年04月19日

嗨，爱思考的PZer你好：


是的，可以这么理解。

spot rate和forward rate的关系如下

（1+S1）(1+f(1,1))=(1+S2)^2。

分子分母两边同时用1除，变为

(1/(1+S1))*(1/(1+f(1,1))=1/(1+S2)^2

(1/(1+S1))代表1年期zero coupon债券的spot price，1/(1+f(1,1)代表 forward price for a one-year zero-coupon bond beginning in one year，

1/(1+S2)^2代表2年期zero coupon 债的spot price。

题目已知S1，1/（1+f(1,1)），让计算1/(1+S2)^2

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