Asian options for local-stochastic volatility models in the short-maturity regime

TL;DR

This paper develops short-maturity asymptotic formulas for Asian option prices in local-stochastic volatility models, providing explicit series expansions and practical approximations for implied volatility features.

Contribution

It introduces a novel expansion method for the variational problem in large deviations, deriving explicit asymptotics and implied volatility approximations for Asian options.

Findings

Asymptotic formulas accurately approximate Asian option prices for small maturities.

Explicit series expansions for the rate function around the ATM point.

Good numerical performance demonstrated in SABR, Heston, and bounded local volatility models.

Abstract

We derive the short-maturity asymptotics for Asian option prices in local-stochastic volatility (LSV) models. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. Using large deviations theory methods, the asymptotics for the OTM options are expressed as a rate function which is represented as a two-dimensional variational problem. We develop a novel expansion method for the variational problem by expanding the rate function around the ATM point. In particular, we derive series expansions in log-moneyness for the solution of this variational problem around the ATM point, and obtain explicit results for the first three terms. We give the ATM volatility level, skew and convexity of the implied volatility of an Asian option in a general local-stochastic volatility model, which can be used as an approximation for pricing Asian options with strikes sufficiently close to the ATM point. Using numerical simulations in the SABR, Heston and an LSV model with bounded local volatility, we show good performance of the asymptotic result for Asian options with sufficiently small maturity.