Asian Option Pricing via Laguerre Quadrature: A Diffusion Kernel Approach

TL;DR

This paper introduces new mathematical techniques involving diffusion equations, potential theory, and special functions to improve Asian option pricing models, offering a novel approach to complex financial derivatives valuation.

Contribution

It develops a diffusion kernel approach using Laguerre quadrature and special functions, advancing the theoretical framework for Asian option pricing.

Findings

Derivation of diffusion equations for Asian options

Application of potential theory to solve complex expressions

Introduction of Whittaker-type confluent hypergeometric functions

Abstract

This paper will demonstrate some new techniques for developing the theory of Asian (arithmetic average) options pricing. We discuss the basic derivation of the diffusion equations, and how various techniques from potential theory can be applied to solve these complex expressions. The Whittaker-type confluent hypergeometric functions are introduced, and we discuss how these functions are related to other systems including Mehler-Fock and modified Bessel functions. We close with a brief analysis of some index transforms and the kernels related to these integral transforms.