Closed-Form Solutions for Fixed-Strike Arithmetic Asian Options

Abstract

This paper establishes exact probability density functions for discretely and continuously monitored arithmetic average prices, assuming asset returns follow a normal distribution. By utilizing a one-step time convolution approach to maturity, we derive real-time efficient closed-form pricing formulas for geometric-normal discretely and continuously monitored arithmetic Asian options. Furthermore, we extend this methodology to accommodate  Lѐvy asset returns processes, enabling the precise pricing of discretely and continuously monitored fixed-strike arithmetic Asian options via univariate closed-form integrals.

Keywords: Fixed-strike arithmetic Asian options, closed-form formulas, geometric-normal and Lévy processes

JEL Classification: G13