Euro Stoxx 50 Black Scholes 定价

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据我所知， Euro Stoxx 50属于price index,这种股票是需要分发股息分红的，还有种叫performance index,不分发股息，而是将其重新投资在股票里。
问题来了》
关于black scholes modell里的公式，对于Euro Stoxx 50这种price index的定价是
C=S*N(d1)-X*e-r(T-t)*N(d2)
还是要考虑股息率的定价:

C=S*e-d(T-t)N(d1)-X*e-r(T-t)*N(d2)


什么时候公式里要考虑股息率呢，请解释，谢谢啦~~

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关键词：SCHOLES choles Black Holes euro Black

You have to use the BS model with dividend payment if the underlying asset pays dividend.

For index, since there are many stocks inside, the dividend payment can be regard as continuous, so that you can just estimate the expected dividend rate according to the historical data (say, 1%) then put into the BS model and calculate the option's price.

Chemist_MZ 发表于 2013-4-19 09:55
You have to use the BS model with dividend payment if the underlying asset pays dividend.

For in ...

关键是我现在找到的historical data只是各个公司股票的dividend yield.总的euro stoxx 50的historical dividend yield找不到，难道需要根据这个指数里各个公司股票的比重来算？

sushuiasushui 发表于 2013-4-20 00:18
关键是我现在找到的historical data只是各个公司股票的dividend yield.总的euro stoxx 50的historical di ...

yep, you should calculate a weighted average of each stock's dividend. Or for convenience, you can just calculate the equally weighted average.

Chemist_MZ 发表于 2013-4-20 06:07
yep, you should calculate a weighted average of each stock's dividend. Or for convenience, you can ...

我不知道能否找到从发行期到截止期的每个股票的dividend yield.实际上我需要的是annual dividend yield(以百分比的形式)带入相对应的BS模型和衍生品定价公式。
今天搜了一天的google，只搜到stoxx官网的一个数据，还不确定是不是要求的dividend yield。。。
明天继续找，谢谢你给了我一个新思路，用比重的方法来计算，希望能有结果吧

sushuiasushui 发表于 2013-4-20 07:01
我不知道能否找到从发行期到截止期的每个股票的dividend yield.实际上我需要的是annual dividend yield(以 ...

you're welcome

Chemist_MZ 发表于 2013-4-20 07:22
you're welcome

不好意思，再问一下，我在网上发现有euro stoxx 50的Dividend Future的historical price的信息。我认为它的underlying是euro stoxx 50的dividend.
我可以从dividend future的价格来求出它的underlying,也就是dividend,然后除以相对应的euro stoxx 50的股票价格，求出每天的dividend yield。
不知道这个想法对不对？如果对的话，怎么由每天的Dividend yield数据算出Annual dividendyield呢？
[Sum(everyday`s dividend yield)/ the number of days ]*365?
or just use the dividend to calculate:
[Sum of dividends/the number of days]*365/endindex price?
我只是大胆猜测下，因为好像index里的每个股票分发Dividend的日期不同，真不知道怎么算了{:2_36:}

sushuiasushui 发表于 2013-4-20 18:55
不好意思，再问一下，我在网上发现有euro stoxx 50的Dividend Future的historical price的信息。我认为它 ...

OK, I give you an example.

Suppose there are only 3 stocks in the index, and we don't care when it pays the dividend.

Say stock1 pays 1%, stock 2 pays2%, stock 3 pays 1.5%.

For equally weighted portfolio, q is just 1.5%. For weighted average, you just weighted with each stock's capital size.

Actually, in Merton's option pricing formula with dividend payment, the dividend is considered "continuous" which is an impossible assumption which means the firms pays a dividend on every small time interval. For index, since there are many stocks inside, say stock1 one pays on the first day, stock 2 on the second, stock 3 on the third, we can approximately consider it as "continuous".

There is also an option pricing formula for lump sum dividend, but that is more complicated. I don't think you need that.

best,

thank u