The stock of Twoface Co. will either rise to 75 or decline to 62 over the next month. You want to value a call option on Twoface with a strike price of 67, and a time to expiry of one month. The price of a one-month “up” state-contingent claim (paying $1 if Twoface rises, and nothing otherwise) is 0.5455. The price of a one-month “down” state-contingent claim (paying $1 if Twoface falls, and nothing otherwise) is 0.4446.

a. Calculate the risk-free interest rate?
b. What is the value of the call option?