  This paper discusses the short-maturity behavior of Asian option prices and
hedging portfolios. We consider the risk-neutral valuation and the delta value
of the Asian option having a H\"older continuous payoff function in a local
volatility model. The main idea of this analysis is that the local volatility
model can be approximated by a Gaussian process at short maturity $T.$ By
combining this approximation argument with Malliavin calculus, we conclude that
the short-maturity behaviors of Asian option prices and the delta values are
approximately expressed as those of their European counterparts with volatility
$$\sigma_{A}(T):=\sqrt{\frac{1}{T^3}\int_0^T\sigma^2(t,S_0)(T-t)^2\,dt}\,,$$
where $\sigma(\cdot,\cdot)$ is the local volatility function and $S_0$ is the
initial value of the stock. In addition, we show that the convergence rate of
the approximation is determined by the H\"older exponent of the payoff
function. Finally, the short-maturity asymptotics of Asian call and put options
are discussed from the viewpoint of the large deviation principle.

Mathematical Finance