Option pricing and portfolio hedging under the mixed hedging strategy

•We have proposed a mixed hedging strategy to price options.•Risk preference parameter μμ and scaling δtδt have the important influences on the effective cost.•We get that the mixed hedging strategy is better than the delta hedging in some cases.•The relation between scaling and portfolio hedging is discussed.

This paper is concerned in the option pricing and portfolio hedging in a discrete time incomplete market. It has been shown that scaling and residual risks as well as the mixed hedging strategy play an important role in option pricing and portfolio hedging in a discrete time case. In particular, the relation between scaling (i.e., trading frequency) and portfolio hedging is discussed.