Question

Consider the binomial model for an American call and put on a stock whose price is $90. The exercise price for both the put and the call is $65. The standard deviation of the stock returns is 25 percent per annum, and the risk-free rate is 6 percent per annum. The options expire in 120 days. The stock will pay a dividend equal to 4 percent of its value in 60 days. (a) Draw the three-period stock tree and the corresponding trees for the call and the put.

(b) Compute the price of these options using the three-period trees.

(c) Explain when, if ever, each option should be exercised.

Answer 1

Given Data: Stock Price, S= $ 90.00 Exercise Price, put, Xp= $65.00 Call,Xc= $ 65.00 Option expires in 120 days Standard Deviation, Sd= Standard Deviation, Sd= 25% per year 4% for 60 days Risk free rate= Risk free rate= 6% per year 1% for 60 days Dividend pay in 60 days= 4% of stock price = $ 3.60

solution Size of up mone factor , u : core * = 60 days o 60 of down mone filer, D iD=0.90]

Propability of up mone, the sento Probability of down move, Lo - 1-T To = 0.48

$90 12 +2.6$ BaL3 oday 60 days 120 days

53 CA38. 540 - - - २८ मानक ValuN

call option in so baie = cuytho + Carted (86.22 x 052)+(1+0) = $29.5 Victor fotsion In a day y Value of 245 call option today ( 13) 1 Co $29.22

6 Put option to Value of put option is zero as the stock price at all the times is more than the ut exemuse puice $65.

c) The call option should be exercised at 60 days as the value of stock is high and dividend is paid out.