# 2. Suppose some stock currently selling for \$80 will either increase

2. 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.

1. What are u and d?

= \$100/\$80 = 1.25

d = \$64/%80 = 0.80

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).

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

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

0 replies