Wat is Static arbitrage, butterfly and calendar arbitrage?

A static arbitrage in a set of option quotes is a portfolio of the options, the forward and bonds, bought once and held to the expiries, that costs nothing and pays a non-negative amount in every state, positive in some. A butterfly arbitrage is one inside an expiry: call prices that are not convex in the strike, so that a butterfly has a negative price. A calendar arbitrage is one across expiries: a longer-dated option cheaper than the shorter-dated one at the same forward-moneyness.