Second-Order Greeks

Second-order Greeks measure how the first-order Greeks themselves move. Vanna is delta's sensitivity to volatility, volga is vega's sensitivity to volatility, and charm is delta's decay with time. They matter to anyone running a hedged book: vanna and charm flows around large expiries drive real index moves, and a desk that hedges delta but ignores its drift with time and vol will find its hedge quietly wrong every morning.