ACT370 - Final Exam, 2008 Questions 1 and 2 relate to the following ...

8. The option would not be exercised at any node other than nodes 4 or 7 since the stock pricewould be less than 100 at any other node. The prepaid forward price at time 0 is "!! HÐ"Þ!&Ñ. #H #The stock price at node 4 is Ò"!! ÓÐ"Þ"Ñ H œ "#" Þ!*(&!'H .Ð"Þ!&ÑHÐ"Þ!&ÑThe stock price at node 7 is Ò"!! ÓÐ"Þ"Ñ œ "$$Þ"! "Þ#!(#&'H .##The option value at node 7 is #$Þ"! "Þ#!(#&'H , and the option value at node 8 is 0.The exercise value of the option at node 4 is "" Þ!*(&!'H .The binomial tree backward induction value of the option at node 4 isÐÞ(&ÑÐ#$Þ"!"Þ#!(#&'HÑ"Þ!&œ "'Þ& Þ)'#$#'H .Exercise at node 4 will be optimal if "" Þ!*(&!'H "'Þ& Þ)'#$#'H ,or equivalently, if H (Þ"* ÞAnswer: D$9. ? œ RÐ. " Ñ œ Þ'&&% p ." œ Þ% (from the standard normal table).For the option with a strike price of 100, and X œ "ß < œ Þ!) , we have