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四喜 · 2023年04月27日

关于div折现

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=(561(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

我觉得,这里的div只有一笔,不是连续红利,不应该用连续复利折现,应该用反求出来的annual rf=3.0455%折现

1 个答案

Lucky_品职助教 · 2023年04月27日

嗨,努力学习的PZer你好:


这里的复利不是连续复利,只是普通的复利哦,

一般看到libor,FRA,swap就用单利,比如1+5%*4/12这样,利息不再复利;

大多数情况下,一年算若干次利息就是离散复利,比如 (1+5%)^(4/12),

一年算无穷次利息就是连续复利,这里公式要用到e

----------------------------------------------
努力的时光都是限量版,加油!

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