Butterfly-spread arbitrage for nonconvex call prices
= Butterfly-spread arbitrage for nonconvex call prices
{title2=$C(K_2)\leq\tfrac12[C(K_1)+C(K_3)]\quad(K_2=(K_1+K_3)/2)$}
The midpoint butterfly buys half a call at each outer strike and sells one at the middle strike. <Convexity> of $K\mapsto(S-K)^+$ makes its terminal payoff nonnegative. A violation of the displayed price inequality makes its cost negative and creates <arbitrage>. The payoff is triangular between the outer strikes and zero elsewhere.