1. Suppose that, in each period, the cost of a security either goes up by a factor of a = 2 or down by a factor d = 1/2. Assume the initial price of the security is $100 and that the interest rate r is 0 a). Compute the risk neutral probabilities p (price moves up) and q = 1 -p (price moves down) for this mandel uppose in each period, the cast of asecurity like goss oof = $100 r=O b). Assuming the strike price of a European call option on this security is $150, compute the possible A compute risks neutral probabilites p(pice man y ) s payoffs of the call option given that the option expires in two periods. It may help to sketch a diagram of the possible security price movement over two periods. 8= 1 ( Price onmyes dam ) for this model P = (Hr ) - (ud ) c). What is the exported value of the payolf of the call option? p : 1+ 0 - 2- 05 D= 1). What should the no-arbitrage price of the call option be? D Initial price of security $100 Initial price of stock $106 Initial price of security is $100 interest rater) G years period is, ayears and U-2 $100 1 year $ 200 $100 It out 1 aoo Period 10 $ 50 a years $400 4100 $ 25 $ 400 # 100 2 100* 2 So 100: 2 : 200 Sd 100. 4 : 50 100 * 3 $ 50 Sun 200.2 # 400 100 + 2*2 Buy 50.2 = 100 100 *2 + 2 #4 00 $ 100 Sde 50. 2 = 25 10 0 + 12 * = $85 p=(e"(d ) = 0.5 L ( v-d ) 1.5 3 Stock price to go down in