Before revision:  Finance 19 (2009), 1-12] and are valid in great generality, both for extreme strike (with arbitrary bounded maturity, possibly varying with the strike) and for small maturity (with arbitrary strike, possibly varying with the maturity) .
After revision:  Finance 19 (2009), 1-12] . We present applications to popular models, including Carr-Wu finite moment logstable model, Merton's jump diffusion model and Heston's model .