For general time-dependent local volatility models, we propose new approximation formulas for the price of call options. This extends previous results of Benhamou et al. (Int. J. Theor. Appl. Finance 13(4):603–634, 2010) where stochastic expansions combined with Malliavin calculus were performed to obtain approximation formulas based on the local volatility At The Money. Here, we derive alternative expansions involving the local volatility at strike. Averaging both expansions give even more accurate results. Approximations of the implied volatility are provided as well.