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# The Black-Scholes option pricing problem in mathematical finance: generalization and extensions for a large class of stochastic processes

## Author

Listed:
• Jean-Philippe Bouchaud

(Science & Finance, Capital Fund Management
CEA Saclay;)

• Didier Sornette

(UCLA
Science & Finance, Capital Fund Management)

## Abstract

No abstract is available for this item.

## Suggested Citation

• Jean-Philippe Bouchaud & Didier Sornette, 1994. "The Black-Scholes option pricing problem in mathematical finance: generalization and extensions for a large class of stochastic processes," Science & Finance (CFM) working paper archive 500040, Science & Finance, Capital Fund Management.
• Handle: RePEc:sfi:sfiwpa:500040
as

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## References listed on IDEAS

as
1. Michel M. Dacorogna, & Ulrich A. Muller & Olivier V. Pictet & Casper De Vries,, "undated". "The Distribution of Extremal Foreign Exchange Rate Returns in Extremely Large Data Sets," Working Papers 1992-10-22, Olsen and Associates.
2. Jean-Philippe Bouchaud & Didier Sornette & Marc Potters, 1997. "Option pricing in the presence of extreme fluctuations," Science & Finance (CFM) working paper archive 500038, Science & Finance, Capital Fund Management.
Full references (including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. Trinidad Segovia, J.E. & Fernández-Martínez, M. & Sánchez-Granero, M.A., 2012. "A note on geometric method-based procedures to calculate the Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(6), pages 2209-2214.
2. 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.
3. Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2010. "Student's t-Distribution Based Option Sensitivities: Greeks for the Gosset Formulae," Papers 1003.1344, arXiv.org, revised Jul 2010.
4. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "European option pricing under the Student’s t noise with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 848-858.
5. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
6. Jean-Philippe Aguilar & Cyril Coste & Hagen Kleinert & Jan Korbel, 2016. "Regularization and analytic option pricing under $\alpha$-stable distribution of arbitrary asymmetry," Papers 1611.04320, arXiv.org, revised Nov 2016.
7. Kakushadze, Zura, 2017. "Volatility smile as relativistic effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 59-76.
8. Cassidy, Daniel T. & Hamp, Michael J. & Ouyed, Rachid, 2010. "Pricing European options with a log Student’s t-distribution: A Gosset formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5736-5748.
9. J. Doyne Farmer, 1999. "Physicists Attempt to Scale the Ivory Towers of Finance," Working Papers 99-10-073, Santa Fe Institute.
10. Sergei Fedotov & Sergei Mikhailov, 1998. "Option Pricing Model for Incomplete Market," Papers cond-mat/9807397, arXiv.org, revised Aug 1998.
11. Wang, Xiao-Tian, 2010. "Scaling and long range dependence in option pricing, IV: Pricing European options with transaction costs under the multifractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 789-796.
12. D. Sornette, 1998. "String'' formulation of the Dynamics of the Forward Interest Rate Curve," Papers cond-mat/9802136, arXiv.org.
13. Neda Esmaeeli & Peter Imkeller, 2015. "American Options with Asymmetric Information and Reflected BSDE," Papers 1505.05046, arXiv.org, revised Aug 2017.
14. Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2013. "Log Student’s t -distribution-based option sensitivities: Greeks for the Gosset formulae," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1289-1302, July.
15. 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.
16. Wang, Xiao-Tian & Yan, Hai-Gang & Tang, Ming-Ming & Zhu, En-Hui, 2010. "Scaling and long-range dependence in option pricing III: A fractional version of the Merton model with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 452-458.
17. Stephane Crepey, 2004. "Delta-hedging vega risk?," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 559-579.
18. E. Aurell & R. Baviera & O. Hammarlid & M. Serva & A. Vulpiani, 1998. "A general methodology to price and hedge derivatives in incomplete markets," Papers cond-mat/9810257, arXiv.org, revised Apr 1999.
19. Cassidy, Daniel T., 2011. "Describing n-day returns with Student’s t-distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2794-2802.
20. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, June.

### JEL classification:

• G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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