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 Co. with a strike price of 67, and 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?