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 Subject: Pricing an option Category: Business and Money > Finance Asked by: mathdumbie-ga List Price: \$25.00 Posted: 25 Oct 2006 09:47 PDT Expires: 24 Nov 2006 08:47 PST Question ID: 776775
 ```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``` 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?``` 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```
 mathdumbie-ga rated this answer: `Excellent service!`