let ck denote a european vanilla call option with, Other Engineering

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let ck denote a european vanilla call option with

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 (K1) < (K2) < (K3) and 2 (K2) = (K1 + K3)

What are the no-arbitrage lower bound, and the no-arbitrage upper bound, of the vertical spread C(k1) - C(k2) ?

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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