Consider a European capped call option whose terminal payoff function is given by where X is the

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Consider a European capped call option whose terminal payoff function is given by 

CM (S, 0; X, M) = min(max(S - X, 0), M),

where X is the strike price and M is the cap. Show that the value of the European capped call is given by 

CM (S, T; X, M) = c(S, t; X) - c(S, t; X + M),

where c(S,τ ; X + M) is the value of a European vanilla call with strike price X + M.

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