Fractional Order Stochastic Differential Equation with Application in European Option Pricing. (13th August 2014)

• Record Type: Journal Article
• Authors: Li, Qing; Zhou, Yanli; Zhao, Xinquan; Ge, Xiangyu
• Other Names: Li Jianping Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2014(2014)
• Publication Date: 2014-08-13
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2014/621895
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE) model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function) in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.