Summary: In option pricing theory, the well-known duality principle proposes that calculation of risk-neutral prices of call options can be carried out to calculation of risk-neutral prices of put options in corresponding dual models. In the present paper we discuss a number of options in diffusion models, for which we show how the problem of deriving hedging strategies for call options can be transformed into the problem of deriving hedging strategies for put options in dual models. We consider also Magrabe options and some exotic options.