## option's

vandana.jain
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Posts: 41
Joined: Tue Jul 24, 2012 4:56 pm

### option's

A European call option on a dividend paying stock is priced at \$4 and has a strike price of \$20. The stock is trading at \$20 and is supposed to deliver a dividend of \$0.80 after 3 and again after 6 months. The risk free interest rate is 7%. Calculate the price of the European put option on the same stock having the same strike price. Both the options are going to expire in 7 months.
a. \$4
b. \$4.76
c. \$4.80
d. \$4.96

what should be the ans...

content.pristine
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Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: option's

Since the Call Price is given, we can use the Put-Call Parity Formula.
However, this is a stock pays a dividend.
We use the formula:
p + S = c + Ke^-rT + PV of Dividends
P = 4 + 20e^(-.07*7/12) + 0.8(e^-0.07*3/12 + e^-0.07*6/12) - 20
P=4.758

swarnendupathak
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Joined: Mon Sep 17, 2012 11:06 am

### Re: option's

Hi,
I think the answer is comming as 3.99.

Thanks
Swarnendu

content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: option's

P= 4 + 20e^(-.07*7/12) + 0.8(e^-0.07*3/12 + e^-0.07*6/12) - 20
P= 4+ 19.1998 + 1.5586 - 20
P=4.7583

How did you get 3.99?

swarnendupathak
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Posts: 119
Joined: Mon Sep 17, 2012 11:06 am

### Re: option's

Hi,
As the question says that, the second dividend is to be paid after 6 months )i.e. 6 months from 3 months or total of 9 months from today), so i didn't consider the present value of second dividend, as it is beyond our problem (i.e. beyond 7 months from today of expiration of contract).
Please correct me if i am wrong.

Swarnendu

content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: option's

Hi Swarnendu,

That is a very interesting observation.
However, in this question, they say "after 3 and again after 6 months. " That means at T=3 and T=6. They didn't mean to say T=3 and T=9. If they were referring to t=9, they would say something like "after 3 and 6 months after the first dividend".. However, I do understand your confusion.. It is possible you face similar confusions in the actual exam. Take care for this..