Assume that the current stock price is $45. The stock price in one year can be either $62 or $25. The risk-free rate is 2%.

(a) Calculate today's value of a one-year European call option on the stock with exercise price of $38 by using the binomial option pricing model. Explicitly calculate the replicating portfolio. Show your calculations.

(b) Calculate today's value of a one-year European call option on the stock with exercise price of $38 by using risk-neutral probabilities. Explicitly calculate the risk-neutral probability of the stock price moving to $62. Show your calculations.