A Semianalytical Solution of the Fractional Derivative Model and Its Application in Financial Market
Author
Abstract
Suggested Citation
DOI: 10.1155/2018/1872409
Download full text from publisher
References listed on IDEAS
- Robert C. Merton, 2005.
"Theory of rational option pricing,"
World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288,
World Scientific Publishing Co. Pte. Ltd..
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007.
"Fractional diffusion models of option prices in markets with jumps,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
- Alvaro Cartea & Diego del-Castillo-Negrete, 2006. "Fractional Diffusion Models of Option Prices in Markets with Jumps," Birkbeck Working Papers in Economics and Finance 0604, Birkbeck, Department of Economics, Mathematics & Statistics.
- Giona, Massimiliano & Eduardo Roman, H., 1992. "Fractional diffusion equation for transport phenomena in random media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 87-97.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
- Jumarie, Guy, 2008. "Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 271-287, February.
- Benoit Mandelbrot, 2015.
"The Variation of Certain Speculative Prices,"
World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78,
World Scientific Publishing Co. Pte. Ltd..
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394-394.
- Benoit B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290, National Bureau of Economic Research, Inc.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Sivaporn Ampun & Panumart Sawangtong, 2021. "The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Haq, Sirajul & Hussain, Manzoor, 2018. "Selection of shape parameter in radial basis functions for solution of time-fractional Black–Scholes models," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 248-263.
- Brandi, Giuseppe & Di Matteo, T., 2022. "Multiscaling and rough volatility: An empirical investigation," International Review of Financial Analysis, Elsevier, vol. 84(C).
- Jean-Philippe Aguilar & Jan Korbel & Nicolas Pesci, 2021. "On the Quantitative Properties of Some Market Models Involving Fractional Derivatives," Mathematics, MDPI, vol. 9(24), pages 1-24, December.
- Turvey, Calum G., 2001. "Random Walks And Fractal Structures In Agricultural Commodity Futures Prices," Working Papers 34151, University of Guelph, Department of Food, Agricultural and Resource Economics.
- Wang, Jun & Liang, Jin-Rong & Lv, Long-Jin & Qiu, Wei-Yuan & Ren, Fu-Yao, 2012. "Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 750-759.
- Seemann, Lars & Hua, Jia-Chen & McCauley, Joseph L. & Gunaratne, Gemunu H., 2012. "Ensemble vs. time averages in financial time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6024-6032.
- Carmen López-Martín & Sonia Benito Muela & Raquel Arguedas, 2021. "Efficiency in cryptocurrency markets: new evidence," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(3), pages 403-431, September.
- Menn, Christian & Rachev, Svetlozar T., 2005. "A GARCH option pricing model with [alpha]-stable innovations," European Journal of Operational Research, Elsevier, vol. 163(1), pages 201-209, May.
- Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
- He, Xue-Zhong & Li, Youwei, 2015.
"Testing of a market fraction model and power-law behaviour in the DAX 30,"
Journal of Empirical Finance, Elsevier, vol. 31(C), pages 1-17.
- Xue-Zhong He & Youwei Li, 2015. "Testing of a Market Fraction Model and Power-Law Behaviour in the Dax 30," Research Paper Series 354, Quantitative Finance Research Centre, University of Technology, Sydney.
- Ghysels, E. & Harvey, A. & Renault, E., 1995.
"Stochastic Volatility,"
Papers
95.400, Toulouse - GREMAQ.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," LIDAM Discussion Papers CORE 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
- Eric Ghysels & Andrew Harvey & Eric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
- repec:uts:finphd:40 is not listed on IDEAS
- Zhu, Ke & Ling, Shiqing, 2015.
"Model-based pricing for financial derivatives,"
Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
- Zhu, Ke & Ling, Shiqing, 2014. "Model-based pricing for financial derivatives," MPRA Paper 56623, University Library of Munich, Germany.
- Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
- Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
- Hua, Jia-Chen & Chen, Lijian & Falcon, Liberty & McCauley, Joseph L. & Gunaratne, Gemunu H., 2015. "Variable diffusion in stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 221-233.
- Yoshio Miyahara & Alexander Novikov, 2001. "Geometric Lévy Process Pricing Model," Research Paper Series 66, Quantitative Finance Research Centre, University of Technology, Sydney.
- David H. Pyle., 1997. "Bank Risk Management: Theory," Research Program in Finance Working Papers RPF-272, University of California at Berkeley.
- Brisset, Nicolas, 2017.
"On Performativity: Option Theory And The Resistance Of Financial Phenomena,"
Journal of the History of Economic Thought, Cambridge University Press, vol. 39(4), pages 549-569, December.
- Nicolas Brisset, 2016. "On Performativity: Option Theory and the Resistance of Financial Phenomena," GREDEG Working Papers 2016-31, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
- Lv, Longjin & Xiao, Jianbin & Fan, Liangzhong & Ren, Fuyao, 2016. "Correlated continuous time random walk and option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 100-107.
- Goddard, John & Onali, Enrico, 2012.
"Self-affinity in financial asset returns,"
International Review of Financial Analysis, Elsevier, vol. 24(C), pages 1-11.
- John Goddard & Enrico Onali, 2014. "Self-affinity in financial asset returns," Papers 1401.7170, arXiv.org.
Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:1872409. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.