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show that for any constant 0a1 cak1 1-ak2

Show that for any constant 0=a=1,
C(aK1 + (1-a)K2) = aC(K1) + (1-a)C(K2)
where C(k) is the European option price with strike K. All the options in this question are assumed to be written on the same stock, and have same maturity date. Note: The butterfly is a special case when a=0.5.

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