The probability distribution of returns in the exponential Ornstein-Uhlenbeck model

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2008, Issue 11, 2008, Pages

  Bormetti, G ^a,b   Cazzola, V ^a   Montagna, G ^a,b,c   Nicrosini, O ^a,b  

^a SCUOLA UNIVERSITARIA SUPERIORE IUSS PAVIA   (Italy)

^b INFN SEZIONE DI PAVIA   (Italy)

^c UNIVERSITY OF PAVIA   (Italy)

Author keywords

Models of financial markets; Stochastic processes

Indexed keywords

EID: 65549118201     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2008/11/P11013     Document Type: Article

References (46)

1. Bachelier L 1900 Ann. Sci. cole Norm. Sup. 17 21
2. Einstein A 1905 Ann. Phys., NY 17 549
3. von Smoluchowski M 1906 Ann. Phys., NY 21 756
4. Langevin P 1908 C. R. Acad. Sci. 146 530
5. Uhlenbeck G E and Ornstein L S 1930 Phys. Rev. 36 823
6. Kramers H A 1940 Physica 7 284
7. Risken H The Fokker-Planck equation: Methods of Solution and Applications (Berlin: Springer)
8. Brigo D and Mercurio F 2006 Interest Rate Models-Theory and Practice: with Smile, Inflation and Credit (Berlin: Springer)
9. Black F and Scholes M 1973 J. Polit. Economy 72 637
10. Scott L 1987 J. Financ. Quant. Anal. 22 419
11. Hull J and White A 1987 J. Finance 42 281
12. Stein E and Stein J 1991 Rev. Financ. Stud. 4 727
13. Heston S L 1993 Rev. Financ. Stud. 6 327
14. Ball C and Roma A 1994 J. Financ. Quant. Anal. 29 589
15. Fouque J P, Papanicolaou G and Sircar K R 2000 Derivatives in Financial Markets with Stochastic Volatility (Cambridge: Cambridge University Press)
16. Carr P and Madan D 1999 J. Comput. Finance 2 61
17. Lewis A L 2001 A simple option formula for general jump-diffusion and other exponential Lévy processes Available at SSRN: http://ssrn.com/ abstract = 282110
18. Bouchaud J P and Potters M 2000 Theory of Financial Risk and Derivative Pricing: from Statistical Physics to Risk Management (Cambridge: Cambridge University Press)
19. Bacry E, Delour J and Muzy J F 2001 Phys. Rev. E 64 026103
20. Draglescu A A and Yakovenko V M 2002 Quant. Finance 2 443
21. Masoliver J and Perelló J 2002 Int. J. Theor. Appl. Finance 5 541
22. Masoliver J, Perelló J and Anento N 2004 Physica A 344 134
23. Borland L, Bouchaud J P, Muzy J F and Zumbach G 2005 Wilmott 16 263
24. Borland L and Bouchaud J P 2005 On a multi-timescale statistical feedback model for volatility fluctuations arXiv:physics.soc-ph/0507073
25. Masoliver J and Perelló J 2006 Quant. Finance 6 423
26. Cisana E, Fermi L, Montagna G and Nicrosini O 2007 A comparative study of stochastic volatility models arXiv:0709.0810 [physics.soc-ph]
27. Bonanno G, Valenti D and Spagnolo B 2007 Phys. Rev. E 75 016106
28. Valenti D, Spagnolo B and Bonanno G 2007 Physica A 382 311
29. Perelló J, Sircar R and Masoliver J 2008 Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model arXiv:0804.2589 [physics.soc-ph]
30. Fouque J P, Papanicolaou G and Sircar K R 2000 Int. J. Theoretical Appl. Finance 3 101
31. Bouchaud J P, Matacz A and Potters M 2001 Phys. Rev. Lett. 87 228701
32. Masoliver J, Perelló J and Bouchaud J P 2004 Appl. Math. Finance 11 27
33. Bormetti G and Cazzola V 2008 in preparation
34. Gardiner C W 1983 Handbook of Stochastic Methods (Berlin: Springer)
35. Cramér H 1951 Mathematical Methods of Statistics (Princeton, NJ: Princeton University Press)
36. Jondeau E, Poon S H and Rockinger M 2007 Financial Modeling Under Non-Gaussian Distributions (Berlin: Springer)
37. Glasserman P 2003 Monte Carlo Methods in Financial Engineering (Berlin: Springer)
38. Adams J, Brom T and Layton J 2007 Microwulf: breaking the 100 USD/GFLOP barrier Available at: http://www.clustermonkey.net
39. Albrecher H, Mayer P, Schoutens W and Tistaert J 2007 Wilmott 27 83
40. Kahl C and Jäckel P 2005 Wilmott 19 94
41. Lord R and Kahl C 2006 Why the rotation count algorithm works Tinbergen Institute Discussion Paper
42. Pasquini M and Serva M 2000 Eur. Phys. J. B 16 195
43. Mantegna R and Stanley H E 2000 An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge: Cambridge University Press)
44. Potters M, Cont R and Bouchaud J 1998 Europhys. Lett. 41 239
45. Duffie D, Pan J and Singleton K 2000 Econometrica 68 1343
46. Filho G B and Rosenfeld R 2004 Physica A 344 484