Suppose you apply the two-period Binomial Option Pricing model for a European call option (with strike price as $15.50) on a non-dividend-paying stock. The time to maturity is 3 months and the current stock price is $16.20 and the risk-free rate is 2.5%. Let the possible gain and loss of the underlying stock price be given as the following states:

Gain: the percentage of gain is 45%

Loss: the percentage of loss is -20%

Answer the following questions:

a) How much is the risk-neutral probability in the Binomial Option Pricing model in this case? Why are they called risk-neutral probability? Do they represent the genuine probabilities of the possible gain and loss of the stock price?

b) How much is the fair value of the call option? What about the value of put option?

c) Does the Binomial Option Pricing model consider the volatility of the underlying stock?