  We present a rigorous study of the short maturity asymptotics for Asian
options with continuous-time averaging, under the assumption that the
underlying asset follows a local volatility model. The asymptotics for
out-of-the-money, in-the-money, and at-the-money cases are derived, considering
both fixed strike and floating strike Asian options. The asymptotics for the
out-of-the-money case involves a non-trivial variational problem which is
solved completely. We present an analytical approximation for Asian options
prices, and demonstrate good numerical agreement of the asymptotic results with
the results of Monte Carlo simulations and benchmark test cases in the
Black-Scholes model for option parameters relevant in practical applications.
