Hello!
At last, here's the answer :)
First of all, I'll assume that the standard deviation you provide is
for annual returns. That said, you can find the Black-Scholes formula
at the following site:
Wikipedia
http://en.wikipedia.org/wiki/Black-Scholes
Let's first compute "d1" and "d2" as described in that link. Using the
same notation, you have:
S = 20
K = 25
T = 2
r = 0.05
sigma = 0.8
Plugging these value into the formula gives:
d1 = 0.4568408747...
d2 = -0.6745299752...
Now, the formula for the options value makes use of the standard
normal cummulative distribution function (cdf). Since there is no
explicit formula for this function, I used the online calculator at
the following site:
Normal Calculator
http://cnx.rice.edu/content/m11328/latest/
[make sure you select "Area left of" in this calculator]
Finally, plugging d1 and d2 in the calculator, and using these results
in the call value formula, we get that the theoretical value of the
call option , according to this model, is:
C = 7.86
Likewise, the theoretical value of the put option is:
P = 10.48
If you want to take a shortcut, you can just use the follwing
Java-based online European option value calculator
Option pricing
http://www.margrabe.com/OptionPricing.html
If you plug the parameters of your problem, you'll get the same
results as with the formula (probably a bit different because I did
some rounding).
Regarding the 80%, forget what I said in the clarification request
about it being quite high. There are lots of stocks with volatility
even higher than 80% annualy.
Google search terms
black scholes formula
://www.google.com.ar/search?hl=es&q=black+scholes+formula&meta=
option calculator black scholes
://www.google.com.ar/search?hl=es&q=option+calculator+black+scholes&meta=
I hope this helps! If you have any questions regarding my answer,
please don't hesitate to request a clarification. Otherwise I await
your rating and final comments.
Best wishes!
elmarto |