  We derive the short-maturity asymptotics for option prices in the local
volatility model in a new short-maturity limit $T\to 0$ at fixed $\rho = (r-q)
T$, where $r$ is the interest rate and $q$ is the dividend yield. In cases of
practical relevance $\rho$ is small, however our result holds for any fixed
$\rho$. The result is a generalization of the Berestycki-Busca-Florent formula
for the short-maturity asymptotics of the implied volatility which includes
interest rates and dividend yield effects of $O(((r-q) T)^n)$ to all orders in
$n$. We obtain analytical results for the ATM volatility and skew in this
asymptotic limit. Explicit results are derived for the CEV model. The
asymptotic result is tested numerically against exact evaluation in the
square-root model model $\sigma(S)=\sigma/\sqrt{S}$, which demonstrates that
the new asymptotic result is in very good agreement with exact evaluation in a
wide range of model parameters relevant for practical applications.
