Past exam of the mathematics course of the University of Cambridge 2014 iii Paper 38 4 b Solution Created 2026-10-03 Updated 2026-10-06
Buy half a call at each neighboring strike and sell one call at the middle strike. Its cost isFor fixed terminal stock price , the function is convex. Since is the midpoint, the payoffis nonnegative for every . More explicitly, it is zero outside , equals on , and equals on . The negative cost and nonnegative payoff produce an arbitrage. This is the butterfly-spread arbitrage for nonconvex call prices.