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四喜 · 2023年04月30日

如题

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NO.PZ201702190300000304

问题如下:

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:

中文解析:

根据题干信息可知,当前的市场上关于Alpha公司的看涨期权是被高估的,因此套利操作下我们可以卖出被高估的买进被低估的,因此正如本题问题中表述的已经卖出了看涨期权,然后需要的操作是买入一个合成的看涨期权。

看涨期权的合成相当于借钱买股票,因此本题选B。

题干说了是short call,直接用ck=ps不就好了吗,感觉解析说的太复杂了吧

1 个答案
已采纳答案

pzqa27 · 2023年05月04日

嗨,努力学习的PZer你好:


C+K=P+S做个变形是-C=K-P-S,这个并不能帮我们选出正确答案,解析这个思路不能说是最简单的,但是是最正确的思考方式,这个题与其说是考察put call parity,不如说是考察delta hedge

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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!

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NO.PZ201702190300000304问题如下 For the Alpha Company option, the positions to take aantage of the arbitrage opportunity are to write the call an A.short shares of Alpha stoanlenB.buy shares of Alpha stoanborrow.C.short shares of Alpha stoanborrow. B is correct.You shoulsell (write) the overpricecall option anthen go long (buy) the replicating portfolio for a call option. The replicating portfolio for a call option is to buy h shares of the stoanborrow the present value of (hS- - c-).c = hS + PV(-hS- + c-).h = (- 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 overpriceat, say, 4.50, you short the option anhave a cash flow Time 0 of +4.50. You buy the replicating portfolio of 0.60 shares 50 per share (giving you a cash flow of -30) anborrow (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 Time 0 is + 4.50 - 3.713 = 0.787. Your net cash flow Time 1 for either the up move or wn move is zero. You have ma arbitrage profit of 0.787.In tabulform, the cash flows are follows:中文解析根据题干信息可知,当前的市场上关于Alpha公司的看涨期权是被高估的,因此套利操作下我们可以卖出被高估的买进被低估的,因此正如本题问题中表述的已经卖出了看涨期权,然后需要的操作是买入一个合成的看涨期权。看涨期权的合成相当于借钱买股票,因此本题选我读懂了这道题要short call, 但我疑惑write the call是指啥?

2024-10-25 23:33 1 · 回答

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