Let C (K ) denote a European vanilla Call option with strike price K. Assume that all options are identical except for strike price, and strike prices satisfy K_{1 }< K_{2} < K_{3} and 2K_{2} = K_{1} + K_{3}.
problem 1: ?What are the no-arbitrage lower bound, and the no-arbitrage upper bound, of the vertical spread:
C(K_{1}) − C(K_{2})?
problem 2: Derive the functional relationship between the no-arbitrage values of the two vertical spreads:
C(K_{1}) − C(K_{2}) and C(K_{2}) − C(K_{3}).