3. Consider a one-period binomial world in which the current stock price of 40 can either go up by 15 percent or down by 20 percent. There is a European call option on this stock with an exercise price of 40 expiring at the end of first period. The risk-free rate is 10 percent. a. Calculate the stock and call prices and risk neutral probabilities for both up and down positions along the tree. Show all your work. b. What is the theoretical value of the call at time 0 , i.e., today? Show all your work. c. Calculate the hedge ratio and interpret the number. d. Suppose a dealer quotes a call price (premium) of $4.00. Using your results in parts b and c, describe the arbitrage transactions for the investor and calculate the amount of arbitrage profit. Show your work