Short Maturity Asian Options in Local Volatility Models

TL;DR

This paper derives short maturity asymptotics for Asian options under local volatility models, providing analytical approximations and validating them with numerical simulations.

Contribution

It offers a rigorous derivation of asymptotics for Asian options in local volatility models, including solutions to complex variational problems.

Findings

Asymptotic formulas match Monte Carlo results closely.

Analytical approximations are effective for practical parameters.

Solutions cover out-of-the-money, at-the-money, and in-the-money cases.

Abstract

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.