On arbitrage and replication in the fractional Black–Scholes pricing model

Citations

Cited by:

1. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2017. "Pricing derivatives in Hermite markets," Papers 1709.09068, arXiv.org.
2. Yue Qi & Yue Wang, 2023. "Innovating and Pricing Carbon-Offset Options of Asian Styles on the Basis of Jump Diffusions and Fractal Brownian Motions," Mathematics, MDPI, vol. 11(16), pages 1-22, August.
3. Calisse, Frank, 2019. "The impact of long-range dependence in the capital stock on interest rate and wealth distribution," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203591, Verein für Socialpolitik / German Economic Association.
4. Wang, Xiao-Tian, 2011. "Scaling and long-range dependence in option pricing V: Multiscaling hedging and implied volatility smiles under the fractional Black–Scholes model with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1623-1634.
5. Erhan Bayraktar & H. Vincent Poor & K. Ronnie Sircar, 2004. "Estimating The Fractal Dimension Of The S&P 500 Index Using Wavelet Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(05), pages 615-643.
   • Erhan Bayraktar & H. Vincent Poor & Ronnie Sircar, 2007. "Estimating the Fractal Dimension of the S&P 500 Index using Wavelet Analysis," Papers math/0703834, arXiv.org.
6. Wang, Xiao-Tian, 2010. "Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 438-444.
7. Foad Shokrollahi, 2017. "The valuation of European option with transaction costs by mixed fractional Merton model," Papers 1702.00152, arXiv.org.
8. Yamada, Toshihiro, 2015. "A formula of small time expansion for Young SDE driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 64-72.
9. Xiao, Weilin & Zhang, Weiguo & Xu, Weijun & Zhang, Xili, 2012. "The valuation of equity warrants in a fractional Brownian environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1742-1752.
10. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
11. Jani Lukkarinen & Mikko S. Pakkanen, 2016. "Arbitrage without borrowing or short selling?," Papers 1604.07690, arXiv.org, revised Oct 2016.
12. Ehsan Azmoodeh, 2010. "On the fractional Black-Scholes market with transaction costs," Papers 1005.0211, arXiv.org.
13. Axel A. Araneda, 2019. "The fractional and mixed-fractional CEV model," Papers 1903.05747, arXiv.org, revised Jun 2019.
14. Gapeev Pavel V. & Sottinen Tommi & Valkeila Esko, 2011. "Robust replication in H-self-similar Gaussian market models under uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 37-50, March.
15. Mikko S. Pakkanen & Jani Lukkarinen, 2016. "Arbitrage without borrowing or short selling?," CREATES Research Papers 2016-13, Department of Economics and Business Economics, Aarhus University.
16. Luis G. Gorostiza & Reyla A. Navarro & Eliane R. Rodrigues, 2004. "Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems," RePAd Working Paper Series lrsp-TRS401, Département des sciences administratives, UQO.
17. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2019. "Pricing Derivatives In Hermite Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-27, September.
    • Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2016. "Pricing Derivatives in Hermite Markets," Papers 1612.07016, arXiv.org, revised Dec 2016.
    • Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2017. "Pricing derivatives in Hermite markets," Papers 1709.09068, arXiv.org.
18. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009, January-A.
19. Kerstin Lamert & Benjamin R. Auer & Ralf Wunderlich, 2025. "Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(2), pages 163-218, April.
20. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.
21. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
22. Rostek, S. & Schöbel, R., 2013. "A note on the use of fractional Brownian motion for financial modeling," Economic Modelling, Elsevier, vol. 30(C), pages 30-35.
23. Matthieu Garcin, 2019. "Fractal analysis of the multifractality of foreign exchange rates [Analyse fractale de la multifractalité des taux de change]," Working Papers hal-02283915, HAL.
24. Azmoodeh Ehsan & Mishura Yuliya & Valkeila Esko, 2009. "On hedging European options in geometric fractional Brownian motion market model," Statistics & Risk Modeling, De Gruyter, vol. 27(02), pages 129-144, December.
25. Foad Shokrollahi, 2018. "Pricing European option with the short rate under Subdiffusive fractional Brownian motion regime," Papers 1805.00792, arXiv.org.
26. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.