This chapter introduces the hedging and pricing of options. Delta hedging of options is defined and it is explained how oscillations in the underlying can lead to gamma profits for the market maker. The gains and losses on an option position are shown to be related to a partial differential equation which is shown to be one of several ways of deriving the Black–Scholes option pricing equation. Barrier options are discussed as extensions of simple plain vanilla call and put options. The Greeks (delta, gamma, vega, and theta) are defined and the concept of gamma trading and volatility trading is discussed. Real-life complications related to smile effects and the term structure of volatility are pointed out.