Question 14 You have learned the various concepts involving call and put options before. One of the usefulness of these concepts involves the replication of investments and the analysis of their payotts. One of such replications involves the following strategies: Going long on a stock (S) and a put option (P) and Going long on a zero-coupon bond (K) with the face value equaling to the strike price (K) given the yield (i) and time to maturity (T) and long on the call option (C). Required: a) Show that the payoffs strategies discussed above are the same. Assume that these options are European options and the put, call and face value of the zero coupon bond have the same strike price (K) and the time to maturity is followed. (You do not need to graph these payoffs). (4 marks) b) Since the payoffs for both strategies are the same, then we can equate the two strategies as follows: S+P - (1+OM Using the equation above, explain how an investor could design a synthetic (artificial) portfolio that would replicate someone 1. Buying a stock (a portfolio that has the same payoff as an investor who is buying a stock) (3 marks) 2 Buying a zero-coupon bond (a portfolio that has the same payoff as an Investor who is buying a ZCB): (3 marks) 3. Buying a put (a portfolio that has the same payoff as an investor who is buying a put option); (3 marks) 4. Buying a call a portfolio that has the same payoff as an investor who is buying a call option) (3 marks) SFNCEDOZWISVD/S4/2021 Page 10 of 17 c) Suppose that the current stock price is $52 and the risk-free rate is 5% p.a. You have found a quote for a 3-month put option with an exercise price of 50. The put price is 1.50, but due to the light trading in the call option, there was not a listed quote for the 3-month, 50 call. Estimate the price of the 3-month call option (4 marks) (Total: 20 marks)