Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications. (12th March 2020)

• Record Type: Journal Article
• Authors: Lv, Longjin; Wang, Luna
• Other Names: Di Bella Beatrice Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2020(2020)
• Publication Date: 2020-03-12
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2020/7168571
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : In this paper, we first investigate the stochastic representation of the modified advection-dispersion equation, which is proved to be a subordinated stochastic process. Taking advantage of this result, we get the analytical solution and mean square displacement for the equation. Then, applying the subordinated Brownian motion into the option pricing problem, we obtain the closed-form pricing formula for the European option, when the underlying of the option contract is supposed to be driven by the subordinated geometric Brownian motion. At last, we compare the obtained option pricing models with the classical Black–Scholes ones.