Series representation of the pricing formula for the European option driven by space-time fractional diffusion
Author
Abstract
Suggested Citation
Download full text from publisher
References listed on IDEAS
- Kleinert, H. & Korbel, J., 2016. "Option pricing beyond Black–Scholes based on double-fractional diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 200-214.
- Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
- Jizba, Petr & Kleinert, Hagen & Haener, Patrick, 2009. "Perturbation expansion for option pricing with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3503-3520.
- Peter Carr & Liuren Wu, 2003.
"The Finite Moment Log Stable Process and Option Pricing,"
Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
- Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, University Library of Munich, Germany.
- Jizba, Petr & Korbel, Jan & Lavička, Hynek & Prokš, Martin & Svoboda, Václav & Beck, Christian, 2018. "Transitions between superstatistical regimes: Validity, breakdown and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 29-46.
- 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.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
- Jean-Philippe Aguilar, 2017. "A series representation for the Black-Scholes formula," Papers 1710.01141, arXiv.org, revised Oct 2017.
- Laurent E. Calvet & Adlai Fisher, 2008. "Multifractal Volatility: Theory, Forecasting and Pricing," Post-Print hal-00671877, HAL.
- Gong, Xiaoli & Zhuang, Xintian, 2017. "American option valuation under time changed tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 57-68.
- Hagen Kleinert & Jan Korbel, 2015. "Option Pricing Beyond Black-Scholes Based on Double-Fractional Diffusion," Papers 1503.05655, arXiv.org, revised Mar 2016.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Pedro Febrer & João Guerra, 2021. "Residue Sum Formula for Pricing Options under the Variance Gamma Model," Mathematics, MDPI, vol. 9(10), pages 1-29, May.
- Jean-Philippe Aguilar & Justin Lars Kirkby & Jan Korbel, 2020. "Pricing, Risk and Volatility in Subordinated Market Models," Risks, MDPI, vol. 8(4), pages 1-27, November.
- 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.
- Jean-Philippe Aguilar & Jan Korbel, 2019. "Simple Formulas for Pricing and Hedging European Options in the Finite Moment Log-Stable Model," Risks, MDPI, vol. 7(2), pages 1-14, April.
- Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
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.- 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.
- Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
- Jean-Philippe Aguilar & Jan Korbel, 2019. "Simple Formulas for Pricing and Hedging European Options in the Finite Moment Log-Stable Model," Risks, MDPI, vol. 7(2), pages 1-14, April.
- Jean-Philippe Aguilar & Cyril Coste & Jan Korbel, 2016. "Non-Gaussian analytic option pricing: a closed formula for the L\'evy-stable model," Papers 1609.00987, arXiv.org, revised Nov 2017.
- Juan M. Romero & Ilse B. Zubieta-Mart'inez, 2016. "Relativistic Quantum Finance," Papers 1604.01447, arXiv.org.
- Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Finance and Stochastics, Springer, vol. 26(4), pages 733-769, October.
- Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006.
"Pricing and Inference with Mixtures of Conditionally Normal Processes,"
Working Papers
2006-28, Center for Research in Economics and Statistics.
- Bertholon, H. & Monfort, A. & Pegoraro, F., 2007. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working papers 188, Banque de France.
- Jianhui Li & Sebastian A. Gehricke & Jin E. Zhang, 2019. "How do US options traders “smirk” on China? Evidence from FXI options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(11), pages 1450-1470, November.
- Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
- Ricardo Crisóstomo, 2017. "Speed and biases of Fourier-based pricing choices: Analysis of the Bates and Asymmetric Variance Gamma models," CNMV Working Papers CNMV Working Papers no. 6, CNMV- Spanish Securities Markets Commission - Research and Statistics Department.
- Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
- Shuang Li & Yanli Zhou & Yonghong Wu & Xiangyu Ge, 2017. "Equilibrium approach of asset and option pricing under Lévy process and stochastic volatility," Australian Journal of Management, Australian School of Business, vol. 42(2), pages 276-295, May.
- Carr, Peter & Wu, Liuren, 2004.
"Time-changed Levy processes and option pricing,"
Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
- Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, University Library of Munich, Germany.
- Feng, Chengxiao & Tan, Jie & Jiang, Zhenyu & Chen, Shuang, 2020. "A generalized European option pricing model with risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
- Gonçalo Faria & João Correia-da-Silva, 2014.
"A closed-form solution for options with ambiguity about stochastic volatility,"
Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.
- Gonçalo Faria & João Correia-da-Silva, 2011. "A Closed-Form Solution for Options with Ambiguity about Stochastic Volatility," FEP Working Papers 414, Universidade do Porto, Faculdade de Economia do Porto.
- Edwards, Craig, 2006. "Integrating delta: An intuitive single-integral approach to pricing European options on diverse stochastic processes," Economics Letters, Elsevier, vol. 92(1), pages 20-25, July.
- F. Cacace & A. Germani & M. Papi, 2019. "On parameter estimation of Heston’s stochastic volatility model: a polynomial filtering method," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 503-525, December.
- Jingzhi Huang & Liuren Wu, 2004.
"Specification Analysis of Option Pricing Models Based on Time- Changed Levy Processes,"
Finance
0401002, University Library of Munich, Germany.
- Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes," Econometric Society 2004 North American Winter Meetings 405, Econometric Society.
- Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
- Young Shin Kim & Kum-Hwan Roh & Raphael Douady, 2022.
"Tempered stable processes with time-varying exponential tails,"
Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 541-561, March.
- Young Shin Kim & Kum-Hwan Roh & Raphael Douady, 2020. "Tempered Stable Processes with Time Varying Exponential Tails," Papers 2006.07669, arXiv.org, revised Aug 2020.
- Raphaël Douady & Young Shin Kim & Kum-Hwan Roh, 2021. "Tempered stable processes with time-varying exponential tails," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03512709, HAL.
- Young Shin Aaron Kim & Kum-Hwan Roh & Raphaël Douady, 2020. "Tempered Stable Processes with Time Varying Exponential Tails," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03018495, HAL.
- Raphaël Douady & Young Shin Kim & Kum-Hwan Roh, 2021. "Tempered stable processes with time-varying exponential tails," Post-Print hal-03512709, HAL.
- Young Shin Aaron Kim & Kum-Hwan Roh & Raphaël Douady, 2020. "Tempered Stable Processes with Time Varying Exponential Tails," Working Papers hal-03018495, HAL.
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:arx:papers:1712.04990. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.