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蛋黄也酥酥 · 2021年05月12日

The replicating portfolio for a call option is to buy h shares of the stock and borrow the present value of (hS- - c-).

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NO.PZ201702190300000304

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:

这句话我的理解是long call=long h shares and short bond(borrow)

但是题目中是put call,所以我选反了。

这样理解有什么不对呢。

另外从哪里看出这个是被高估了

1 个答案

WallE_品职答疑助手 · 2021年05月14日

嗨,爱思考的PZer你好:


the positions to take advantage of the arbitrage opportunity are to write the call 已经告诉你需要short call option,但正常来说我们是需要判断是long call还是short call来套利。


就这一题来说,它已经告诉你是short call。在此基础上套利,套利就是risk free且自己不出钱。

首先 满足risk free: short call当股票价格下降时有风险,所以我们需要long stock来hedge。所以需要long stock而不是short stock,这样可以直接锁定B答案。

然后,一份call option需要delta份股票hedge,所以1份call option需要买0.6份股票hedge。short 1份 call option 可以拿到4.5,买入0.6份股票需要50*0.6=30,钱不够,所以需要borrow。


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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

未命名 · 2021年12月29日

首先 满足risk free: short call当股票价格下降时有风险 上面这句话写错了吧,应该是 short call当股票价格上升时有风险

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