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 e^r1 = 1.1.] A 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 two-step binomial tree.

Question 1

What are u and d?

Question 2

What are the payoffs from the call in each state of the world?

Question 3

What is the European call option price at time 0?

Question 4

What are the pseudoprobabilities of the up and down movements in the stock price?

Question 5

What is the European put option price at time 0?

Hint: (Since the stock currently selling for $80 will either increase in value over the next year to $100, or decrease in value to $64, we know that 80*u^2=100. The volatility is calculate by formula u=exp(Volatility*Sqrt(t)), where t=0.5 in the two step tree, so we can back up the volatility.)