Consider an n = 1 step binomial tree with T = .5. Suppose r, the annualized risk-free rate is 8 %, and delta, the annualized dividend rate is 7 %. Also suppose the annualized standard deviation of the continuously compounded stock return, sigma, is 45 %. Suppose further that the initial stock price, S = $ 90; and that the strike price K is $ 122. Suppose you observe a put price of $ 30.228, which is lower than the price for the European put option that you computed using the 1-step binomial tree method. By using the arbitrage method outlined in the book, that is, selling a synthetic put option and buying the actual put option:



a) Determine the European put premium ?



b) Determine the number of shares of stock that you'll buy ?



c) Determine the amount of money that you'll borrow ?



d) Determine the risk free profit from this arbitrage opportunity ?