Question

The current price of MB Industries stock is $20 per share. In the next year the stock price will either go up to $24 per share or go down to $16 per share. MB pays no dividends. The one year risk-free rate is 5 percent and will remain constant. Using the one-step binomial pricing model, what is the price of a one-year CALL option on MB stock with a strike price of $20 (out to two decimal places)?

Answer 1

The up-move factor U = 24/20 = 1.2

The down-move factor D = 16/20 = 0.8

The probability of up-move p(u) is given by =

r is the risk-free rate = 0.05

t is the time of step = 1 year

p(u) = (e^(0.05*1) - 0.8)/(1.2-0.8) = 0.6281777

The probability of down-move p(d) = 1-0.6281777 = 0.3718223

Option payoff incase of up-move of stock price to $24 = $24-$20 = $4

Option payoff incase of down-move of stock price to $16 = $0 ( Call option expires out of the money)

Expected payoff today = (0.6281777*$4) + (0.3718223*$0)

Expected payoff today = $2.51