Asian Option Pricing Formula for Uncertain Financial Market

TLDR

Asian options are widely used risk‑management derivatives, and in uncertain finance asset prices are modeled by uncertain differential equations rather than stochastic ones. The paper proposes Asian option models for uncertain financial markets. The authors derive Asian option pricing formulas, analyze their properties, and employ the Yao‑Chen formula to compute the average‑price term. Numerical examples demonstrate the applicability of the derived pricing formulas.

Abstract

Asian option is an important financial derivative instrument. It has been widely accepted by investors for its risk management property. Uncertain finance is a new field where the risk processes are described by uncertain processes. An asset price is assumed to follow a specific uncertain differential equation other than a stochastic differential equation. In this paper, Asian option models are proposed for uncertain financial market. Besides, Asian option pricing formulae are derived and some mathematical properties are investigated. Since the average price is presented in the Asian pricing formula which is difficult to compute, Yao-Chen formula is employed to solve this problem. Finally, several numerical examples are discussed.