A stock price is currently $50. It is known that at the end of two months it will be either go up by 6% or go down by 4%. The risk-free interest rate is 10% per annum with continuous compounding. Please use the one-period binomial tree risk-neutral valuation method to answer question (a) and (b). You can directly use the one-period binomial tree risk-neutral probability and risk-neutral valuation formula without deriving them again.

(a) What is the value of a two-month European call option with a strike price of $49, in the arbitrage-free economy?

(b) What is the value of a two-month European put option with a strike price of $49, in the arbitrage-free economy?

(c) Verify your answer in part (b) using put-call parity