Consider a modified butterfly option position, Butterfly = C(K1,T) - a C(K,T) + C(K3,T), with K...

 

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Consider a modified butterfly option position, Butterfly = C(K1,T) - a C(K,T) + C(K3,T), with K < K < K3 and a > 0. a) How can we choose a to guarantee a vanishing payoff for S = K and S = K3? b) It is possible to generalize a butterfly position even more to the form Butterfly = C(K, T) a C(K, T) + b C(K3, T), with K < K < K3 and a, b > 0. How can we choose the coefficients a and b to generate a vanishing payoff for ST K and ST K3? Consider a modified butterfly option position, Butterfly = C(K1,T) - a C(K,T) + C(K3,T), with K < K < K3 and a > 0. a) How can we choose a to guarantee a vanishing payoff for S = K and S = K3? b) It is possible to generalize a butterfly position even more to the form Butterfly = C(K, T) a C(K, T) + b C(K3, T), with K < K < K3 and a, b > 0. How can we choose the coefficients a and b to generate a vanishing payoff for ST K and ST K3?