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Junqi · 2020年11月23日

问一道题:NO.PZ201702190300000304

* 问题详情,请 查看题干

问题如下:

4.For the Alpha Company option, the positions to take advantage of the arbitrage opportunity are to write the call and:

选项:

A.

short shares of Alpha stock and lend.

B.

buy shares of Alpha stock and borrow.

C.

short shares of Alpha stock and borrow.

解释:

B is correct.

You should sell (write) the overpriced call option and then go long (buy) the replicating portfolio for a call option. The replicating portfolio for a call option is to buy h shares of the stock and borrow the present value of (hS- - c-).

c = hS + PV(-hS- + c-).

h = (c+ - c-)/(S+ - S-) = (6 - 0)/(56 - 46) = 0.60.

For the example in this case, the value of the call option is 3.714. If the option is overpriced at, say, 4.50, you short the option and have a cash flow at Time 0 of +4.50. You buy the replicating portfolio of 0.60 shares at 50 per share (giving you a cash flow of -30) and borrow (1/1.05) x [(0.60 x 46) - 0] = (1/1.05) x 27.6 = 26.287. Your cash flow for buying the replicating portfolio is -30 + 26.287 = -3.713. Your net cash flow at Time 0 is + 4.50 - 3.713 = 0.787. Your net cash flow at Time 1 for either the up move or down move is zero. You have made an arbitrage profit of 0.787.

In tabular form, the cash flows are as follows:

既然call option overpriced那么应该short call,那根据BSM model, short call= short stock + long bond, long bond=借钱出去。麻烦能看一下这个思路为什么不对么?


1 个答案

xiaowan_品职助教 · 2020年11月23日

嗨,努力学习的PZer你好:


同学你好,

题目的目标是通过套利赚取差价,那么此时市场上call是overpriced,我们的操作应该是:

short call并且long一个合理定价的call,才能赚取到差价,题干中已经说了策略的前半部分,write call,所以选项中描述的是怎样合成一个合理定价的call。


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