This paper extends the static hedging portfolio (SHP) approach of Derman et al., 1995, Carr et al., 1998 to price and hedge American knock-in put options under the Black–Scholes model and the constant elasticity of variance (CEV) model. We use standard European calls (puts) to construct the SHPs for American up-and-in (down-and-in) puts. We also use theta-matching condition to improve the performance of the SHP approach. Numerical results indicate that the hedging effectiveness of a bi-monthly SHP is far less risky than that of a delta-hedging portfolio with daily rebalance. The numerical accuracy of the proposed method is comparable to the trinomial tree methods of Ritchken, 1995, Boyle and Tian, 1999. Furthermore, the recalculation time (the term is explained in Section 1) of the option prices is much easier and quicker than the tree method when the stock price and/or time to maturity are changed.