Some asymptotics for short maturity Asian options

TL;DR

This paper analyzes the asymptotic behavior of short-maturity Asian options using large deviations theory within a local volatility model that includes jumps, providing estimates for different moneyness scenarios.

Contribution

It introduces a large deviations framework for short-maturity Asian options in a jump-augmented local volatility model, deriving asymptotics for various moneyness levels.

Findings

Out-of-the-money Asian options are governed by rare events.

Provides bounds for at-the-money Asian option asymptotics.

Enhances pricing efficiency for short maturities.

Abstract

Most of the existing methods for pricing Asian options are less efficient in the limit of small maturities and small volatilities. In this paper, we use the large deviations theory for the analysis of short-maturity Asian options. We present a local volatility model for the underlying market that incorporates a jump term in addition to the drift and diffusion terms. We estimate the asymptotics for the out-of-the-money, in-the-money, and at-the-money short-maturity Asian call and put options. Under appropriate assumptions, we show that the asymptotics for out-of-the-money Asian call and put options are governed by rare events. For the at-the-money Asian options, the result is more involved and in that case, we find the upper and lower bounds of the asymptotics of the Asian option price.