Suppose a non-dividend paying stock now sells at $100, and its price will be either $120 or $90 one year later. The risk-free rate is 9.531% per annum with continuous compounding (or equivalently 10% with annual compounding (or e0.095311=1.10-1=10%). Consider a one-year European put option on the stock with a strike price of $110. What should be the number of shares needed to construct a replicating portfolio for one long put, according to the binomial pricing model? (A) -1/4 (B) -1/3 (C) -2/3 (D) -3/4

21. Continuing with question 20, what should be the lending amount (or investment in a zero-coupon bond) needed to form a replicating portfolio for one long put? (A) 36.36 (B) 54.55 (C) 72.73 (D) 81.82

22. Continuing with question 20, what is the risk-neutral probability that the stock price will end up in the up state ($120) one year later? (A) 1/3 (B) 1/4 (C) 2/3 (D) 3/4

23. Continuing with question 20, what should be the price of a one-year European call option on the same underlying stock with the same strike price ($110)? (A)$4.55 (B)$6.06 (C) $ 12.12 (D) $18.18

24. Continuing with question 20, if the risk-adjusted rate of return for this stock is 14% with annual compounding, what is the expected actual probability that the stock price will end up in the up state ($120) one year later? (A) 0.4 (B) 0.6 (C) 0.7 (D) 0.8 (Hint: Solve for the actual probability using the discounted cash flow model for the underlying stock, given the current stock price and the expected prices one year later) 25. If the underlying asset of the one-year European call option in question 20 is a futures option on the non-dividend paying stock. Assume the binomial tree for the futures price is the same as that of the non-dividend paying stock, what is the risk-neutral probability that the expected futures price will end up in the up state ($120) one year later? (A) 1/3 (B) 1/4 (C) 2/3 (D) 3/4