Morse Potential, Contour Integrals, and Asian Options

TL;DR

This paper derives normalized eigenfunctions for the Morse potential using contour integrals, proves their completeness, and applies this spectral method to price Asian options in financial markets.

Contribution

It introduces a contour integral approach to obtain and normalize eigenfunctions for the Morse potential and applies this to Asian option pricing.

Findings

Eigenfunctions for Morse potential are properly normalized.

Completeness relation for the eigenfunctions is explicitly proved.

Spectral decomposition is successfully applied to Asian option pricing.

Abstract

Completeness of the eigenfunctions of a quantum mechanical system is crucial for its probability interpretation. By using the method of contour integral we give properly normalized eigenfunctions for both discrete and continuum spectrum of the Morse potential, and explicitly prove the completeness relation. As an application we use our spectral decomposition formula to study the problem of the pricing of an Asian option traded in financial markets.