Reference no: EM132886101
Suppose some stock currently selling for $80 will either increase in value over the next year to $100, or decrease in value to $64. The risk free rate over the period is 10% given annual compounding. [Let r denote the continuously compounded rate per year. Thus er×1 = 1.1.] A European call option on the stock with an exercise price of $75 matures in one period (1 year). If you want to price the option with a one-step binomial tree.
Question 1. What are u and d?
u = $100/$80 = 1.25
d = $64/%80 = 0.80
Question 2. What are the payoffs from the call in each state of the world?
If stock rises to $100 next year, the payoff will be $25 ($100 - $75). If stock decreases to $64 next year, the payoff will be $0 ($64 - $75).
Question 3. What is the European call price at time 0?
= (c1+r)-D/(U-D)
= (1.1 - 0.8) / (1.25 - 0.8)
= .6666 (probability of up)
Call price at t0 = (.6666 * 25 + 0) / 1.1 = $15.15
Question 4. What are the pseudoprobabilities of the up and down movements in the stock price?
= (c1+r)-D/(U-D)
= (1.1 - 0.8) / (1.25 - 0.8)
= 66.66% probability of up
= (1 - .6666)
= 33.33% probability of down