problems: Let C (K) denote a European vanilla Call option with strike price K. Suppose 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 among the no-arbitrage values of the two vertical spreads C (K_{1}) - C (K_{2}) and C (K_{2}) - C (K_{3}).