Asian Option Pricing under Uncertain Volatility Model

TL;DR

This paper investigates the asymptotic behavior of Asian option prices under uncertain volatility, proposing an approximation method for the nonlinear PDE involved in worst-case scenarios.

Contribution

It introduces a novel approximation approach for Asian option pricing under uncertain volatility by simplifying the nonlinear PDE into two Black-Scholes-like equations.

Findings

Provides a procedure to approximate Asian option prices with small volatility intervals.

Offers a method to solve the fully nonlinear PDE via boundary conditions and equation splitting.

Enhances understanding of Asian option behavior under volatility uncertainty.

Abstract

In this paper, we study the asymptotic behavior of Asian option prices in the worst case scenario under an uncertain volatility model. We give a procedure to approximate the Asian option prices with a small volatility interval. By imposing additional conditions on the boundary condition and cutting the obtained Black-Scholes-Barenblatt equation into two Black-Scholes-like equations, we obtain an approximation method to solve the fully nonlinear PDE.