Short Maturity Forward Start Asian Options in Local Volatility Models

TL;DR

This paper derives short maturity asymptotics for forward start Asian options in local volatility models, providing explicit formulas and asymptotic behaviors for different moneyness scenarios.

Contribution

It introduces a large deviations approach to analyze the exponential decay of option prices and simplifies the rate function calculation in the Black-Scholes model.

Findings

Explicit asymptotic formulas for out-of-the-money, in-the-money, and at-the-money options.

Closed-form rate function in the Black-Scholes model.

Asymptotic behaviors for extreme strike prices.

Abstract

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.