Options and Future

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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 $85 matures in one period (1 year). If you want to price the option with a two-step binomial tree.

1. What are u and d?

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

3. What is the European call price at time 0?

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

5. What is the European put price at time 0?

6. What is the American put price at time 0?