Parameter estimation for time-fractional Black-Scholes equation with S &P 500 index option

Article


An, Xingyu, Wang, Qingxia (Jenny), Liu, Fawang, Anh, Vo V. and Turner, Ian W.. 2023. "Parameter estimation for time-fractional Black-Scholes equation with S &P 500 index option." Numerical Algorithms. 95, pp. 1-30. https://doi.org/10.1007/s11075-023-01563-4
Article Title

Parameter estimation for time-fractional Black-Scholes equation with S &P 500 index option

ERA Journal ID671
Article CategoryArticle
AuthorsAn, Xingyu, Wang, Qingxia (Jenny), Liu, Fawang, Anh, Vo V. and Turner, Ian W.
Journal TitleNumerical Algorithms
Journal Citation95, pp. 1-30
Number of Pages30
Year2023
PublisherSpringer
Place of PublicationUnited States
ISSN1017-1398
1572-9265
Digital Object Identifier (DOI)https://doi.org/10.1007/s11075-023-01563-4
Web Address (URL)https://link.springer.com/article/10.1007/s11075-023-01563-4
AbstractThis paper aims to estimate the parameters of the time-fractional Black-Scholes (TFBS) partial differential equation with the Caputo fractional derivative by using the real option prices of the S &P 500 index options. First, the numerical solution is obtained by developing a high-order scheme with order () for the time discretisation. Some theoretical analyses such as stability and convergence are presented in order to verify the efficiency and accuracy of the proposed scheme. Secondly, we employ a modified hybrid Nelder-Mead simplex search and particle swarm optimization (MH-NMSS-PSO) to identify the fractional order and implied volatility of the TFBS equation, and explore the financial meanings of under extreme stock market conditions such as the Covid-19 and the 2008 global financial crisis. We analyse the values of and compare the mean squared errors of both the TFBS model and the BS model. Our empirical results show that may be regarded as a market fluctuation indicator for classifying financial environments, and the TFBS model is more capable of fitting real option data compared with the BS model, especially for put options during the economic downturn. In addition, we find and discuss an interesting relation between and from both the TFBS model and the BS model in three expressions, which could be an open problem for further research.
KeywordsEmpirical studies; Parameter estimation; Time-fractional Black-Scholes ; Option pricing; Empirical studies
ANZSRC Field of Research 2020350202. Finance
Byline AffiliationsQueensland University of Technology
Centre for Applied Climate Sciences
School of Business
Swinburne University of Technology
Permalink -

https://research.usq.edu.au/item/z2541/parameter-estimation-for-time-fractional-black-scholes-equation-with-s-p-500-index-option

Download files


Published Version
s11075-023-01563-4.pdf
File access level: Anyone

  • 4
    total views
  • 1
    total downloads
  • 0
    views this month
  • 0
    downloads this month

Export as

Related outputs

Are Vietnamese coffee farmers willing to pay for weather index insurance?
Lan, Le, Mushtaq, Shahbaz, Wang, Qingxia (Jenny), Barlis, Angelica, Deniau, Aline, Mittahalli Byrareddy, Vivekananda, Anh, Huynh Tan and Swaans, Kees. 2024. "Are Vietnamese coffee farmers willing to pay for weather index insurance?" International Journal of Disaster Risk Reduction. 100. https://doi.org/10.1016/j.ijdrr.2023.104185
An Introduction to Programming Physics-Informed Neural Network-Based Computational Solid Mechanics
Bai, Jinshuai, Jeong, Hyogu, Batuwatta-Gamage, C. P., Xiao, Shusheng, Wang, Qingxia, Rathnayaka, C.M., Alzubaidi, Laith, Liu, Gui-Rong and Gu, Yuantong. 2023. "An Introduction to Programming Physics-Informed Neural Network-Based Computational Solid Mechanics." International Journal of Computational Methods. 20 (10). https://doi.org/10.1142/S0219876223500135
Do Farmers Demand Innovative Financial Products? A Case Study in Cambodia
Wang, Qingxia, Soksophors, Yim, Phanna, Khieng, Barlis, Angelica, Mushtaq, Shahbaz, Rodulfo, Danny and Swaans, Kees. 2023. "Do Farmers Demand Innovative Financial Products? A Case Study in Cambodia." Journal of Risk and Financial Management. 16 (8). https://doi.org/10.3390/jrfm16080353
Large blockholders and stock price crash risk: An international study
Eugster, Nicolas and Wang, Qingxia (Jenny). 2023. "Large blockholders and stock price crash risk: An international study." Global Finance Journal. 55. https://doi.org/10.1016/j.gfj.2022.100799
Financial effects of carbon risk and carbon disclosure: A review
Wang, Qingxia (Jenny). 2023. "Financial effects of carbon risk and carbon disclosure: A review." Accounting and Finance. 63, pp. 4175-4219. https://doi.org/10.1111/acfi.13090
Investors’ Greed and Fear: An Event Study of Analyst Recommendations
Wang, Qingxia (Jenny). 2022. "Investors’ Greed and Fear: An Event Study of Analyst Recommendations." Haron, Razali (ed.) Financial Crises - Challenges and Solutions. IntechOpen. pp. 1-17
Willingness to Pay for Weather-Indexed Insurance: Evidence from Cambodian Rice Farmers
Wang, Qingxia, Soksophors, Yim, Barlis, Angelica, Mushtaq, Shahbaz, Phanna, Khieng, Swaans, Cornelis and Rodulfo, Danny. 2022. "Willingness to Pay for Weather-Indexed Insurance: Evidence from Cambodian Rice Farmers." Sustainability. 14 (21), pp. 1-17. https://doi.org/10.3390/su142114558
Finite Element Modelling Epoxy/Clay Nanocomposites
Chia, Julian Y. H., Hbaieb, Kais and Wang, Q. X.. 2007. "Finite Element Modelling Epoxy/Clay Nanocomposites." Key Engineering Materials. 334-335, pp. 785-788. https://doi.org/10.4028/www.scientific.net/KEM.334-335.785
Techniques for Efficient Analytical and Simulation Methods in the Prototyping of MEMS Systems
Su, Y., Chong, C. S., Wang, Q. X. and Li, Hua. 2006. "Techniques for Efficient Analytical and Simulation Methods in the Prototyping of MEMS Systems." Leondes, Cornelius T. (ed.) MEMS/NEMS: Handbook Techniques and Applications. United States. Springer. pp. 293-334
Dynamic response of a laminated pipeline on the seabed subjected to underwater shock
Lam, K. Y., Zong, Z. and Wang, Q. X.. 2003. "Dynamic response of a laminated pipeline on the seabed subjected to underwater shock." Composites Part B: Engineering. 34 (1), pp. 59-66. https://doi.org/10.1016/S1359-8368(02)00072-0
Constitutive model development and micro-structural topology optimisation for Nafion hydrogel membranes with ionic clustering
Li, Hua, Yuan, Z., Ng, T. Y., Lee, H. P., Lam, K. Y., Wang, Q. X., Wu, Shunnian, Fu, Jie and Hanes, Justin. 2003. "Constitutive model development and micro-structural topology optimisation for Nafion hydrogel membranes with ionic clustering." Journal of Biomaterials Science: Polymer Edition. 14 (11), pp. 1181-1196. https://doi.org/10.1163/156856203322553428
A variation of local point interpolation method (vLPIM) for analysis of microelectromechanical systems (MEMS) device
Li, Hua, Wang, Q. X. and Lam, K. Y.. 2004. "A variation of local point interpolation method (vLPIM) for analysis of microelectromechanical systems (MEMS) device." Engineering Analysis with Boundary Elements. 28 (10), pp. 1261-1270. https://doi.org/10.1016/j.enganabound.2003.08.008
A novel meshless approach – Local Kriging (LoKriging) method with two-dimensional structural analysis
Lam, K. Y., Wang, Q. X. and Li, Hua. 2003. "A novel meshless approach – Local Kriging (LoKriging) method with two-dimensional structural analysis." Computational Mechanics. 33 (3), pp. 235-244. https://doi.org/10.1007/s00466-003-0524-2
Development of a new meshless — point weighted least-squares (PWLS) method for computational mechanics
Wang, Q. X., Li, Hua and Lam, K. Y.. 2004. "Development of a new meshless — point weighted least-squares (PWLS) method for computational mechanics." Computational Mechanics. 35 (3), pp. 170-181. https://doi.org/10.1007/s00466-004-0611-z
A pseudo-elastic local meshless method for analysis of material nonlinear problems in solids
Gu, Y. T., Wang, Q. X., Lam, K. Y. and Dai, K. Y.. 2007. "A pseudo-elastic local meshless method for analysis of material nonlinear problems in solids." Engineering Analysis with Boundary Elements. 31 (9), pp. 771-782. https://doi.org/10.1016/j.enganabound.2006.12.008
A meshless local Kriging method for large deformation analyses
Gu, Y. T., Wang, Q. X. and Lam, K. Y.. 2007. "A meshless local Kriging method for large deformation analyses." Computer Methods in Applied Mechanics and Engineering. 196 (9-12), pp. 1673-1684. https://doi.org/10.1016/j.cma.2006.09.017
Meshless Simulation of Equilibrium Swelling/Deswelling of PH-Sensitive Hydrogels
Wang, Q. X., Li, H. and Lam, K. Y.. 2005. "Meshless Simulation of Equilibrium Swelling/Deswelling of PH-Sensitive Hydrogels." Journal of Polymer Science Part B: Polymer Physics. 44 (2), pp. 326-337. https://doi.org/10.1002/polb.20698
A nonlinear fluid-structure interaction analysis of a near-bed submarine pipeline in a current
Lam, K. Y., Wang, Q. X. and Zong, Z.. 2002. "A nonlinear fluid-structure interaction analysis of a near-bed submarine pipeline in a current." Journal of Fluids and Structures. 16 (8), pp. 1177-1191. https://doi.org/10.1006/jfls.2002.0463
Development of a novel meshless Local Kriging (LoKriging) method for structural dynamic analysis
Li, Hua, Wang, Q. X. and Lam, K. Y.. 2004. "Development of a novel meshless Local Kriging (LoKriging) method for structural dynamic analysis." Computer Methods in Applied Mechanics and Engineering. 193 (23-26), pp. 2599-2619. https://doi.org/10.1016/j.cma.2004.01.010
Probabilistic failure of a cracked submarine pipeline and subjected to the underwater shock
Lam, K. Y., Zong, Z. and Wang, Q. X.. 2001. "Probabilistic failure of a cracked submarine pipeline and subjected to the underwater shock." Journal of Offshore Mechanics and Arctic Engineering. 123 (3), pp. 134-140. https://doi.org/10.1115/1.1376715
Analysis of microelectromechanical systems (mems) by meshless local kriging (lokriging) method
Wang, Qing Xia, Li, Hua, Lam, Khin Yong and Gu, Yuan Tong. 2004. "Analysis of microelectromechanical systems (mems) by meshless local kriging (lokriging) method." Journal of the Chinese Institute of Engineers. 27 (4), pp. 573-583. https://doi.org/10.1080/02533839.2004.9670905
Modelling stiffness of polymer/clay nanocomposites
Hbaieb, K., Wang, Q. X., Chia, Y. H. J. and Cotterell, B.. 2007. "Modelling stiffness of polymer/clay nanocomposites." Polymer. 48 (3), pp. 901-909. https://doi.org/10.1016/j.polymer.2006.11.062
Analysis of microelectromechanical systems (MEMS) devices by the meshless point weighted least-squares method
Wang, Q. X., Li, Hua and Lam, K. Y.. 2007. "Analysis of microelectromechanical systems (MEMS) devices by the meshless point weighted least-squares method." Computational Mechanics. 40, pp. 1-11. https://doi.org/10.1007/s00466-006-0077-2
Multiscale simulation of coupled length-scales via meshless method and molecular dynamics
Wang, Q. X., Ng, T. Y., Li, Hua and Lam, K. Y.. 2009. "Multiscale simulation of coupled length-scales via meshless method and molecular dynamics." Mechanics of Advanced Materials and Structures. 16 (1), pp. 1-11. https://doi.org/10.1080/15376490802540242
Realized moments and the cross-sectional stock returns around earnings announcements
Wang, Qingxia, Faff, Robert and Zhu, Min. 2022. "Realized moments and the cross-sectional stock returns around earnings announcements." International Review of Economics and Finance. 79, pp. 408-427. https://doi.org/10.1016/j.iref.2022.02.036
Informational content of options around analyst recommendations
Wang, Qingxia, Faff, Robert and Zhu, Min. 2021. "Informational content of options around analyst recommendations." International Journal of Managerial Finance. https://doi.org/10.1108/IJMF-04-2021-0168
A reverse engineered pitch on Cremers et al. (2015), 'Aggregate jump and volatility risk in the cross-section of stock returns'
Wang, Qingxia (Jenny). 2018. "A reverse engineered pitch on Cremers et al. (2015), 'Aggregate jump and volatility risk in the cross-section of stock returns'." Journal of Accounting and Management Information Systems. 17 (1), pp. 178-185. https://doi.org/10.24818/jamis.2018.01010
A new data-driven topology optimization framework for structural optimization
Zhou, Ying, Zhan, Haifei, Zhang, Weihong, Zhu, Jihong, Bai, Jinshuai, Wang, Qingxia and Gu, Yuantong. 2020. "A new data-driven topology optimization framework for structural optimization." Computers and Structures. 239, pp. 1-16. https://doi.org/10.1016/j.compstruc.2020.106310