  We study the short maturity asymptotics for prices of forward start Asian
options under the assumption that the underlying asset follows a local
volatility model. We obtain asymptotics for the cases of out-of-the-money,
in-the-money, and at-the-money, considering both fixed strike and floating
Asian options. The exponential decay of the price of an out-of-the-money
forward start Asian option is handled using large deviations theory, and is
controlled by a rate function which is given by a double-layer optimization
problem. In the Black-Scholes model, the calculation of the rate function is
simplified further to the solution of a non-linear equation. We obtain closed
form for the rate function, as well as its asymptotic behaviors when the strike
is extremely large, small, or close to the initial price of the underlying
asset.
