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hanfei · 2023年10月08日

e^−rT 不理解

NO.PZ2016082402000028

问题如下:

The current price of stock ABC is $42 and the call option with a strike at $44 is trading at $3. Expiration is in one year. The corresponding put is priced at $2. Which of the following trading strategies will result in arbitrage profits? Assume that the risk-free rate is 10% and that the risk-free bond can be shorted costlessly. There are no transaction costs.

选项:

A.

Long position in both the call option and the stock, and short position in the put option and risk-free bond

B.

Long position in both the call option and the put option, and short position in the stock and risk-free bond

C.

Long position in both the call option and the risk-free bond, and short position in the stock and the put option

D.

Long position in both the put option and the risk-free bond, and short position in the stock and the call option

解释:

ANSWER: C

Answers A and B have payoffs that depend on the stock price and therefore cannot create arbitrage profits. Put-call parity says that cp=32=$1c-p=3-2=\$1 should equals SKerτ=4244×0.9048=$2.19S-Ke^{-r\tau}=42-44\times0.9048=\$2.19. The call option is cheap. Therefore buy the call and hedge it by selling the stock, for the upside. The benefit from selling the stock if S goes down is offset by selling a put.

时间为一年,为什么是Ke^rT 而不是Ke^tT 呢




1 个答案
已采纳答案

pzqa27 · 2023年10月09日

嗨,从没放弃的小努力你好:


解析的S是现在的股票价格42元,K作为执行价格,只有在1年后才能实现,这俩不可以直接相减,应当把未来的K折现到现在才能相减,所以是Ke^rT 

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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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NO.PZ2016082402000028问题如下 The current priof stoAis $42 anthe call option with a strike $44 is trang $3. Expiration is in one year. The corresponng put is price$2. Whiof the following trang strategies will result in arbitrage profits? Assume ththe risk-free rate is 10% anththe risk-free boncshortecostlessly. There are no transaction costs. Long position in both the call option anthe stock, anshort position in the put option anrisk-free bon Long position in both the call option anthe put option, anshort position in the stoanrisk-free bon Long position in both the call option anthe risk-free bon anshort position in the stoanthe put option Long position in both the put option anthe risk-free bon anshort position in the stoanthe call option ANSWER: CAnswers A anB have payoffs thpenon the stopriantherefore cannot create arbitrage profits. Put-call parity says thc−p=3−2=$1c-p=3-2=\$1c−p=3−2=$1 shoulequals S−Ke−rτ=42−44×0.9048=$2.19S-Ke^{-r\tau}=42-44\times0.9048=\$2.19S−Ke−rτ=42−44×0.9048=$2.19. The call option is cheap. Therefore buy the call anhee it selling the stock, for the upsi. The benefit from selling the stoif S goes wn is offset selling a put.还是第一句话call option44 trang 3,这一句话为什么44又在答案里对应的是K值,真的晕了,是我英语太差了吗

2023-03-08 09:27 1 · 回答

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