Part A : A portfolio contains two separate options: P1(K1) and C2(K2). The portfolio is short in P1(K1) and long in C2(K2). Assume that the two European options described above are for the same underlying assets and have the same maturity (T) and have no interim cash flows (i.e. no dividends). Assume that each of the options has a different strike (Ki) such that K1< K2 and that the strikes are equally spaced apart. I. Draw a payoff diagram at expiry of the trading strategy which illustrates what potential payoffs could be generated. Include Axis notation. II. What is the lower boundary for the payoff value of the trading strategy described above for any series of two equally spaced strikes Ki. III. What is the upper boundary for the payoff value of the trading strategy described above for any series of two equally spaced strikes Ki.

Part B : Another portfolio contains three European vanilla options: P1(K1), P2(K2) and C3(K3). The portfolio is long in P1(K1) and C3(K3) and short in P2(K2). Assume that the three European options described above are for the same underlying assets and have the same maturity (T) and have no interim cash flows (i.e. no dividends). Assume that each of the options has a different strike (Ki) such that K1< K2< K3 and that the strikes are equally spaced apart. I. Draw a payoff diagram at expiry of the trading strategy which illustrates what potential payoffs could be generated. Include Axis notation. II. What is the lower boundary for the payoff value of the trading strategy described above for any series of three equally spaced strikes Ki. III. What is the upper boundary for the payoff value of the trading strategy described above for any series of three equally spaced strikes Ki. 2

Part C : Prove the initial value of a forward contract at the beginning of the contract (where t = 0)? Explain why futures contracts may have less “risk” than forward contracts. What features and mechanisms ensure that this is the case?