A portfolio contains four separate European vanilla options: C1(K1), C2(K2), C3(K3) and C4(K4). The portfolio is Long in C1(K1) and C4(K4) and short in C2(K2) and C3(K3). Assume that the four European vanilla call options are for the same underlying asset and have the same maturity (T) and have no interim cash flows (i.e. no dividends). Assume that each of the call options has a different strike (Ki) such that K1< K2< K3< K4 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 four equally spaced strikes Ki.
III. What is the upper boundary for the payoff value of the trading strategy described above for any series of four equally spaced strikes Ki.
IV. What type of volatility would suit this sort of payoff structure?