The Greeks

The Greeks measure how an option's price responds to changes in its inputs.

Delta $\Delta = \partial V / \partial S$: how much the price moves per unit of underlying. The first-order risk; hedge by buying/selling the underlying.Gamma $\Gamma = \partial^2 V / \partial S^2$: how delta changes as $S$ moves. High gamma means delta-hedging needs frequent rebalancing.Vega $\nu = \partial V / \partial \sigma$: sensitivity to volatility.Theta $\Theta = \partial V / \partial t$: time decay. Long options bleed theta; short options earn it.Rho $\rho = \partial V / \partial r$: sensitivity to interest rates. Usually small for short-dated options.

Greek hedging is the daily activity of an options trader. A market maker quoting a delta-neutral book is short gamma, long theta, and earning a spread for warehousing the risk; managing the rebalancing cost is most of the job.