This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ACTSC/STAT 446/846 Midterm 2 Fall 2011 Solutions 1. [14 points] A stock with current price S (0) = 100 is modeled by a binomial model with two timesteps of length h = 0 . 5 year each, using u = e ( r ) h + h and d = e ( r ) h h . The stock pays a continuous dividend at an annual rate of = 8% and has volatility = 0 . 25. The current continuously compounded annual riskfree rate is r = 10%. (a) Determine the value of an American call option on this stock with strike price K = 95, where exercise is allowed at time t = 0 , . 5 or 1 year. Solution: [12pts] We have that u = e ( r ) h + h = 1 . 2054, d = e ( r ) h h = 0 . 8464, and q = e ( r ) hd ud = 0 . 4559 . Hence we have the tree (with payo in [ ]): 100[5] 120 . 54[25 . 54] 145 . 30[50 . 30] & 84 . 64[0] & 102 . 03[7 . 03] & 71 . 64[0] So H (1 , 1) = e. 10 * . 5 (50 . 30 q + 7 . 03(1q )) = 25 . 45 E (1 , 1) =25 . 54 V (1 , 1) =25 . 54 H (1 , 0) = e. 10 * . 5 (7 . 03 q ) = 3 . 05 H (0 , 0) = e. 10 * . 5 (25 . 54 q + 3 . 05(1q )) = 12 . 65 V (0 , 0) =12 . 65 (b) Briey explain how to use your work in (a) to determine if the corresponding European call option would be cheaper, without actually computing its price. Solution: [2pts] The European option would be cheaper since in (a) we found out that E (1 , 1) > H (1 , 1), i.e., we would early exercise in the node (1,1). 2. [11 points] A singleperiod market model includes two securities with initial price ~ S (0) = [1 , 4] and possible values at time 1 given by S (1 , ) = 0 5 2 4...
View
Full
Document
 Spring '09
 Adam

Click to edit the document details