Deriving functional relationship between no-arbitrage values


Questions

Let C(K) denote the European vanilla Call option with strike price K. Suppose that all options are identical except for strike price, and strike prices satisfy K123<< and 2K2=K1+K3
Question 1

What are the no-arbitrage lower bound, and the no-arbitrage upper bound, of the vertical spreadC(K1)-C(K2)?
Question 2

Derive the functional relationship between the no-arbitrage values of the two vertical spreads, C(K1)-C(K2) and C(K2)-C(K3).

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Finance Basics: Deriving functional relationship between no-arbitrage values
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