问一道题：NO.PZ2016082402000028

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. 时间为一年，为什么是Ke^−rT 而不是Ke^tT 呢

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

NO.PZ2016082402000028 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 bonLong position in both the call option anthe put option, anshort position in the stoanrisk-free bonLong 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: C Answers 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. 老师，我想确认一下除了C的另一种套利方法 因为目前put option的市场价格高于根据put-call parity算出的合成价格，所以应该long P合成，short P市场， 其中P合成=C+K-S，所以综上，套利策略应该是long call ，long bonshort stoanshort put，这样对吗？

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 bonLong position in both the call option anthe put option, anshort position in the stoanrisk-free bonLong 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: C Answers 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. 老师好，这道题按照答案C，我理解解题思路应该是下图紫色圈的部分按照put-call parity算出来的C(均衡) =4.187，但目前市场上的C=3，所以就要long C(市场），short C(均衡），而short C(均衡）= -P-S+K，即但是如果按照红色圈的部分按照put-call parity算出来的P(均衡）=0.8128，但目前市场上的P=2，所以就要long P(市场），short P(均衡），而short P(均衡）= -C-K+S，所以这道题还有另外一种套利的方法，即long position in put option anstock, short position in call option anrisk-free bon（虽然答案里没有这个） 想和老师确认一下上面的理解是否正确？