A call option is traded with a strike time of 6 months and a  strike
of  $35.  The current Market price is $30.   It is assumed that the
logarithm of the stock price grows linear at mean rate of 35% per year
and a volatility growth rate which equals the mean rate of growth of
the stock price.  A risk free rate is 8 percents per year.  What is
the current option price?  Assume risk neutrality.

Hello!
Given the assumptions you mention, it's possible to use the
Black-Scholes option pricing formula in order to find the value of
this call option.

You can find this pricing formula at the following link:

Wikipedia - Black-Scholes
http://en.wikipedia.org/wiki/Black-Scholes#The_formula

Notice that, given this formula, the option price is independent of
the mean growth rate of 35% per year; while the volatility (which is
also 35% according to your question) does matter.

Clearly, it's not possible to use the formula by hand, so we'll need a
calculator. You can find an online option pricing calculator at

Black-Scholes Model
http://www.erieri.com/scripts23/blackscholes/blackscholes.exe/main

Enter the following inputs in the boxes:

Stock Asset Price = 30 (because the current market price is $30)
Option Strike Price = 35 (the strike price is $35)
Maturity = 0.5 (the option expires in 6 months, which is the same as 0.5 years)
Risk-Free Rate = 0.08 (the risk-free interest rate is 8%)
Volatility = 0.35 (volatility is the same as the mean growth rate, 35%)

After clicking on "Calculate", we find that the current price of this
call option is approximately $1.64.


If you wish to learn more about the Black-Scholes model, I suggest you
read the entire Wikipedia article, at the same link mentioned above:
http://en.wikipedia.org/wiki/Black-Scholes


Google search terms
black scholes
://www.google.com/search?hl=en&q=black+scholes

black scholes calculator
://www.google.com/search?hl=en&q=black+scholes+calculator


I hope this helps! If you have any doubt regarding my answer, please
don't hesitate to request clarification before rating it. Otherwise, I
await your rating and final comments.

Best wishes!
elmarto

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Request for Answer Clarification by mathdumbie-ga on 25 Oct 2006 19:45 PDT

Thank you for your help, you did answer the question; however, I
failed to restrict the question to NOT use Black Scholes (I am told
that that is not required to answer this question based off of the
distribution model formulated from the mean 35% growth rate).  Can I
pay extra for approaching the same solution from another way?

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Clarification of Answer by elmarto-ga on 26 Oct 2006 05:18 PDT

Hello again!
I'm very sorry that that didn't help. Unfortunately, I'm not familiar
with other option pricing models. I will ask GA to remove my answer
and that you get a full refund. In the future, please remember to
include as many details as possible about your question.

Regards,
elmarto

Excellent service!