Quantum harmonic oscillator in option pricing
Computational Finance
2013-10-24 v2 Mathematical Physics
math.MP
Quantum Physics
Abstract
The Black-Scholes model anticipates rather well the observed prices for options in the case of a strike price that is not too far from the current price of the underlying asset. Some useful extensions can be obtained by an adequate modification of the coefficients in the Black-Scholes equation. We investigate from a mathematical point of view an extension directly related to the quantum harmonic oscillator. In the considered case, the solution is the sum of a series involving the Hermite-Gauss functions. A finite-dimensional version is obtained by using a finite oscillator and the Harper functions. This simplified model keeps the essential characteristics of the continuous one and uses finite sums instead of series and integrals.
Cite
@article{arxiv.1310.4142,
title = {Quantum harmonic oscillator in option pricing},
author = {Liviu-Adrian Cotfas and Nicolae Cotfas},
journal= {arXiv preprint arXiv:1310.4142},
year = {2013}
}