Suppose a stock is currently selling for $50 per share. If the stock gains value, it will gain 30% over the next year. If the stock loses value, it will lose (20)% over the next year. Assume the risk-free rate of interest to be 1%. What is the theoretical value of a one-year call option with a strike price of $50, using the binomial model of option pricing

A) Show the call value utilizing the replicating portfolio method, and explaining your positions in the replicating portfolio.

B) Explain how the replicating portfolio provides the same outcome as the option. That is, show that the payoffs of the fractional share provide the exact same outcomes as the call option outcomes.

C) Show the call value utilizing the probability and expected payoff method.

D) Repeat parts A & C above, using a call option strike price of $30.00