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临江仙 · 2023年09月03日

short forward为什么这么画图?

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

short的话,是在到期日卖出标的,然后收到cash

请教用画图法如何画图?——同时如何理解。


我以前画图法很清晰的,听李老师讲了重新定价之类的后,就弄混了。

1 个答案
已采纳答案

pzqa35 · 2023年09月04日

嗨,努力学习的PZer你好:


在我们进行valuation时,到底是采用画图法还是采用重新定价法,主要可以根据题目的已知条件来选择:如果题目给的是St,那采用画图法会比较方便,如果题目直接给了FPt,那此时直接采用重新定价法会比较方便。

本题中给的是short方,因此它的现金流和long方是完全相反的,那么就是如下的图形:


我们可以这样来理解:在0时刻我short了股票的远期合约,那么在3个月后,我需要以FP0的价格卖出股票,那我收到的现金流就是FP0,付出的是股票,它在3个月后的价格我们用S3来表示。同时我们知道,在第2个月时,会有1美元的股利发放,此时股票还是在我的手里,因为第3个月我才会卖出股票,所以这1美元的股利我是拿得到的。因此在第1个月的valuation计算结果就如上图所示,最终结果为4.7026.

在对forward contract定价或者valuation时,我们首先需要判断的就是头寸,其次再根据题目进行相应的计算。一般情况下,我们都是站在long方的角度去画图,这样比较容易记忆,当头寸是short方时,我们只需要给计算结果加上负号即可。 


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