A stock price is currently $50. It is known that at the end of one year it will be either $40 and $60. The exercise price of a one-year European call option is $55. The risk-free interest rate is 5% per annum.

a. Construct a binomial tree to show the payoff of the call option at the expiration date.

b. Based on the binomial tree model, what is the value of the call option?

c. Address the relation between the binomial tree model and the Black-Scholes model.