求一道期权定价的题

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这个为什么选B啊，麻烦写一下具体的公式。。。。。

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关键词：期权定价

First I have to apologize, I am in the school lab, no Chinese typing software is available to me. I have to type it up in English.

I find out this problem by coincidence. Would you like to post where the question comes from? Different texts use different pricing method.

Due to lacking of background information(question source), my intuition would explain it this way.
Let's assume the stock market it random which means the ups and downs have the same frequency; otherwise, give me some seconds to think about it.
And forget about the interest rate for a second. And lets say the stock price right now is also 30. (Sorry it sounds like not rephrasing the problem, but changing it.)
and then, the put option should have the same price like the call option; however, the disparity between two prices are huge (9 times).  It seems the put option is undervalued.

Well give me more seconds, let me see whether I could work out some better explanation. Still like I suggested, it would help a lot if you post the source of the question.

Thank you~

zzyftpl 发表于 2012-3-30 05:02
First I have to apologize, I am in the school lab, no Chinese typing software is available to me. I  ...

I think you are right. Put option price should be equal to call option price. So undervalued, buy it. This is an easy way to think out this question since it is only a multiple question.

I have a better solution now.
I used the binomial asset pricing model (by Steve E. Shreve from his book Stochastic Calculus for FInance I)
Let's say the stock price right now is 31.
The up factor is u, so if the price of the stock goes up its u*31
The down factor is d, so it's d*31
and we know the relationship of u and d is u*d=1...(I mean it's Shreve's assumption.)

Then the strike price is 30. So the call option price is (31*u-30)/(1+10%) = 5. and we could solve u = 35.5/31. and then d is 31/35.5.  SO....
the put option price is (30-31*d)/1.1....since we have acquired d....we could solve this equation to get the put option price is 2.66325...

The reasonable price for put option is 2.66325...but it is on sale for 0.5....Sounds like an authentic LV bag is priced at 10 RMB....it's undervalued...take a long position of it!!!!

So. that's a solution from idea of the text of Shreve.

Hope it helps a little bit...

according to put-call parity
p=c+PV(K-F)=5+PV(30)-31=1.15>0.5
so the put option is undervalued, buy it!

according to put-call parity
p=c+PV(K-F)=5+PV(30)-31=1.15>0.5
so the put option is undervalued, buy it!

期权平价

股票价格+看跌期权=看涨期权+执行价格/(1+r)^n
r为无风险利率  n为期数
所以
看跌期权=5+30/1.1-31≈1.27

zzyftpl 发表于 2012-3-30 05:02
First I have to apologize, I am in the school lab, no Chinese typing software is available to me. I  ...

是公司财务里的一道题。。。你的方法很巧妙呢，谢谢啦～～～～

avrilrocks 发表于 2012-3-30 06:07
according to put-call parity
p=c+PV(K-F)=5+PV(30)-31=1.15>0.5
so the put option is undervalued, bu ...

懂了，谢谢啦～～～～