Suppose that stock price moves up by 5% (u=1.05) and d=1/u. The current stock price is $50. Dividend is zero. Compute the current value of a European call option with the strike price of $51 in 3 months using both replicating portfolio valuation method and the risk neutral valuation method. The risk free rate is APR 5% with continuous compounding (or, 5% per annum)

a. Draw the dynamics of stock price and option price using the one step binomial tree.

b. Draw the dynamics of the replicating portfolio valuation using the one step binomial tree.

c. Present value of debt (B), the risk-neutral probability (p) and option price (f).

d. Solve for the option price using replicating portfolio valuation approach and risk neutral valuation approach, respectively.

Hand written answers showing work preferably