not able to justify that Joseph's arguments may not be correct. Joshua had always found these ideas a bit intricate and given his lack of recent involvement with the derivative industry, the key ideas in this area had already faded away from his memory. In addition, Joshua was also concerned about an important presentation he is scheduled to make to some of his international clients next week. So, Joshua left Joseph with a book on stochastic calculus for finance that includes some material on stock option valuation. (You have the advantage of a condensed and much simplified version of the treatment attached as an appendix with this case.) After looking through the material, Joseph decides to first consider the problem of valuing the stock options that can be exercised in one year at a strike price of $30. By restricting himself to this simpler case, he hopes that, if his valuation turns out to be far from what the material suggests, he would be in a better position to understand the root cause of the difference. This would also satisfy his penchant for financial analysis, something he has been interested in since the days he started trading securities in financial markets. Joseph values the stock options for the single-year period at approximately $5.21 using his earlier methodology. His intuition is unable to find any flaws in the original assessment. On the other hand, the stock option valuation arguments presented in the book send his mind spinning since they are replete with sophisticated mathematical arguments ideas that he correctly assesses are probably too sophisticated for addressing the problem at hand. Can you help Joseph understand the valuation of his stock options using the treatment available in the appendix? Do you think his valuation reasonable according to your estimates? How does the stock option valuation take into account the probability with which the stock value goes up or down? The following setup helps shed some light on the binomial asset pricing model and its