Pricing of the Geometric Asian Options Under a Multifactor Stochastic Volatility Model

TL;DR

This paper develops simplified pricing formulas for continuous geometric Asian options within a multifactor stochastic volatility model, using asymptotic expansion and perturbation techniques to improve accuracy and capture volatility smiles.

Contribution

It introduces a novel multifactor stochastic volatility framework with asymptotic expansion for pricing GAOs, including explicit formulas and parameter estimation methods.

Findings

Derived first-order approximate pricing formulas for GAOs.

Validated the accuracy of the approximation against market data.

Captured volatility smiles through model parameter estimation.

Abstract

This paper focuses on the pricing of continuous geometric Asian options (GAOs) under a multifactor stochastic volatility model. The model considers fast and slow mean reverting factors of volatility, where slow volatility factor is approximated by a quadratic arc. The asymptotic expansion of the price function is assumed, and the first order price approximation is derived using the perturbation techniques for both floating and fixed strike GAOs. Much simplified pricing formulae for the GAOs are obtained in this multifactor stochastic volatility framework. The zeroth order term in the price approximation is the modified Black-Scholes price for the GAOs. This modified price is expressed in terms of the Black-Scholes price for the GAOs. The accuracy of the approximate option pricing formulae is established, and the model parameter is also estimated by capturing the volatility smiles.