Fractional Order Stochastic Differential Equation with Application in European Option Pricing
Joint Authors
Li, Qing
Zhao, Xinquan
Zhou, Yanli
Ge, Xiangyu
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-13
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Li, Qing& Zhou, Yanli& Zhao, Xinquan& Ge, Xiangyu. 2014. Fractional Order Stochastic Differential Equation with Application in European Option Pricing. Discrete Dynamics in Nature and Society،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-485901
Modern Language Association (MLA)
Li, Qing…[et al.]. Fractional Order Stochastic Differential Equation with Application in European Option Pricing. Discrete Dynamics in Nature and Society No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-485901
American Medical Association (AMA)
Li, Qing& Zhou, Yanli& Zhao, Xinquan& Ge, Xiangyu. Fractional Order Stochastic Differential Equation with Application in European Option Pricing. Discrete Dynamics in Nature and Society. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-485901
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-485901