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SHAO · 2024年07月15日

老师,请教下

NO.PZ2023041003000034

问题如下:

Messer explains, “Of course, with the index moving down 10% in the last twelve months, the payoffs with these options could have been replicated without using options.” Szillat responds, “My understanding is that the payoff would have been the same as the call option if you had purchased 0.5697 index units and lent EUR 356.79 at the 1-year interest rate.”

With respect to his assessment of replicating the option payoff, Szillat is least likely correct about:

选项:

A.

lending EUR 356.79.

B.

using the one-year interest rate.

C.

purchasing 0.5697 index units.

解释:

Szillat is incorrect in his method of replicating the call option. It can be replicated by purchasing the amount of the underlying shares designated by the hedge ratio and then borrowing (not lending) an amount equal to the present value of ((hedge ratio × S–) + c–).

老师,我计算了一下borrow的具体金额,帮看下为什么两种计算方式不一样呢

第一种:PV(h × S- - c-) = (0.5697 * 648 - 0) / 1.03 = 358.41

第二种:PV(h × S+ - c+) = (0.5697 * 828-78) / 1.03 = 382.24

请问哪里出错了呢?

1 个答案
已采纳答案

李坏_品职助教 · 2024年07月15日

嗨,爱思考的PZer你好:



根据上面截图的讲义里的公式,

borrow的具体数量 = PV(-h*S- + C-) = (-0.5697 * 648 + 0)/1.03 = -358.41,按照讲义里的公式,这个负号代表的是borrow,所以borrow了358.41.


也可以用 PV(-h * S+ + C+) = (-0.5697*720*1.15 + 78)/1.03 = -382.24.


你算的数字没有问题,之所出现两种算法不同的结果,是因为这道题给出的条件里面,上涨因子u和下降因子d相乘不等于1,说明这个二叉树的上下分叉并不是完全对称的,用S+和S-分别计算出来的borrow数量之间存在一些误差。


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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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