Problem #1 In a binomial model, a call option and a put option are both written on the same stock. The exercise price of the call option is 30 and the exercise price of the put option is 40. The call options payoffs are 0 and 5 and the put options payoffs are 20 and 5. The price of the call is 2.25 and the price of the put is 12.25. a. What is the riskless interest rate? Assume that the basic period is one year. b. What is the price of the stock today?

Problem #2 All reliable analysts agree that a share of ABC Corp., selling today for $50, will be priced at either $65 or $45 one year from now. They further agree that the probabilities of these events are 0.6 and 0.4, respectively. The market risk-free rate is 6%. What is the value of a call option on ABC whose exercise price is $50 and which matures in one year?

Problem #3 A stock is currently selling for 60. The price of the stock at the end of the year is expected either to increase by 25% or to decrease by 20%. The riskless interest rate is 5%. Calculate the price of a European put on the stock with exercise price 55. Use the binomial option pricing model.