You have performed extensive analysis on a company that has led you to believe that the latest project the company is undertaking will be a huge success and will pay off significantly in the next six months.  The stock is traded on the stock exchange but is not a very liquid one since the company has only been recently listed and its market capitalization is not significant. 

 

You want to maximize your returns so instead of buying the stock, you decide to purchase some American options instead to capitalize on the expected increase in the stock price.  Unfortunately, there are no listed options for this company on the exchange.  You have found a counterparty to write some options over the counter.  The stock is currently trading at $105.  You decide to purchase in-the-money call options with a strike price of $100.  Each period is 3 months long and you decide to purchase six month option contracts.  The 6-month T-bill is priced at $97.78.  You calculate the standard deviation at 50%.  Finally, if the project goes well, you estimate that there will be a dividend of $1.50 per share in three months.  If the project does not go as well as planned, the company will reduce their dividend payment to $0.75 per share.

 

Your potential counterparty who will be selling you the call options offer you a price of $23 per option.  Assuming a perfect market with no bid-ask spreads, should you purchase these options at this price?  Run your analysis using binomial option pricing.  Do you think that this is a fair price?  Why or why not?  Is there a cheaper way to get the same payoff profile other than buying call options?