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alexanderwang · 2024年09月09日

关于期限小于1年的折现率

  1. CFA II
  2. Derivative

NO.PZ2019010402000007

问题如下：

A manager sold an equity forward contract one month ago. The maturity of forward contract is three months. A dividend of $1 will be paid in one month before contract expiration. The annually compounded risk-free rate is 3%. The current spot price of underlying is $56, and the initial forward price is $60. The value of the manager’s position is:

选项：

A.

-4.7026

B.

4.7026

C.

4.8512

解释：

B is correct.

考点：equity forward contract求value

解析：

画图（long方）：

valuelong=(56−1(1+3%)1/12)−60(1+3%)2/12=−4.7026value_{long}=(56-\frac1{{(1+3\%)}^{1/12}})-\frac{60}{{(1+3\%)}^{2/12}}=-4.7026

因为这一题的头寸是short方，所以value=4.7026

老师好，我在答一系列题的时候，对于期限小于1年的折现率如果算产生了一些困惑，以60天为例，有的时候是（1+rf*60/360）(如本题），有的时候是（1+rf）^(60/360)，能否请老师帮忙指出一下我应该是哪里理解出现了偏差。

并请老师帮忙总结一下，什么时候用什么，谢谢！

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李坏_品职助教 · 2024年09月09日

嗨，从没放弃的小努力你好：


（1+rf*60/360）这个叫做单利，是用于与Libor相关的计算题，例如interest rate swap或者FRA合约。


而（1+rf）^(60/360)这个是离散复利，除了上述的两种特殊衍生品之外，其他的普通衍生品就用这种方式即可（如果是外汇相关的衍生品或者equity index衍生品，则需要用到连续复利：e^(rf * 60/360) ）。

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