Stochastic volatility of financial markets as the fluctuating rate of trading: An empirical study

Physica A: Statistical Mechanics and its Applications

Volumn 382, Issue 1, 2007, Pages 278-285

  Silva, A Christian ^a   Yakovenko, Victor M ^a  

^a Bldg 142   (United States)

Author keywords

Heston model; Stochastic volatility; Stock market; Subordination

Indexed keywords

APPROXIMATION THEORY; COMMERCE; COSTS; MARKETING; TIME SERIES ANALYSIS;

CONTINUOUS-TIME RANDOM WALK (CTRW); EMPIRICAL STUDY; EXPONENTIAL TAIL; STOCHASTIC VOLATILITY;

FINANCE;

EID: 34249788685     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2007.03.051     Document Type: Article

References (35)

1. Gopikrishnan P., Plerou V., Amaral L.A.N., Meyer M., and Stanley H.E. Phys. Rev. E 60 (1999) 5305
2. Plerou V., Gopikrishnan P., Amaral L.A.N., Meyer M., and Stanley H.E. Phys. Rev. E 60 (1999) 6519
3. Silva A.C., Prange R.E., and Yakovenko V.M. Physica A 344 (2004) 227
4. Bouchaud J.-P., and Potters M. Theory of Financial Risks (2000), Cambridge University Press, Cambridge
5. Miranda L.C., and Riera R. Physica A 297 (2001) 509
6. McCauley J.L., and Gunaratne G.H. Physica A 329 (2003) 178
7. Kaizoji T. Physica A 343 (2004) 662
8. Remer R., and Mahnke R. Physica A 344 (2004) 236
9. Makowiec D. Physica A 344 (2004) 36
10. Matia K., Pal M., Salunkay H., and Stanley H.E. Europhys. Lett. 66 (2004) 909
11. Vicente R., de Toledo C.M., Leite V.B.P., and Caticha N. Physica A 361 (2006) 272
12. Praetz P.D. J. Bus. 45 (1972) 49
13. Hull J., and White A. J. Finance 42 (1987) 281
14. Heston S.L. Rev. Financial Stud. 6 (1993) 327
15. Fouque J.P., Papanicolaou G., and Sircar K.R. Derivatives in Financial Markets with Stochastic Volatility (2000), Cambridge University Press, Cambridge
16. Feller W. An Introduction to Probability Theory and its Applications vol. II (1971), Wiley, New York
17. Clark P.K. Econometrica 41 (1973) 135
18. Mandelbrot B., and Taylor H.M. Oper. Res. 15 (1967) 1057
19. Ané T., and Geman H. J. Finance 55 (2000) 2259
20. Plerou V., Gopikrishnan P., Amaral L.A.N., Gabaix X., and Stanley H.E. Phys. Rev. E 62 (2000) R3023
21. One may also consider the volume of trades instead of the number of trades. In that case, empirical analysis is technically more complicated, so we limit our consideration to the number of trades.
22. Montroll E.W., and Weiss G.H. J. Math. Phys. 6 (1965) 167
23. Montroll E.W., and Shlesinger M.F. In: Lebowitz J.L., and Montroll E.W. (Eds). Nonequilibrium Phenomena II: From Stochastics to Hydrodynamics (1984), North-Holland, Amsterdam
24. Mainardi F., Raberto M., Gorenflo R., and Scalas E. Physica A 287 (2000) 468
25. Sabatelli L., Keating S., Dudley J., and Richmond P. Eur. Phys. J. B 27 (2002) 273
26. Masoliver J., Montero M., and Weiss G.H. Phys. Rev. E 67 (2003) 021112
27. Dremin I.M., and Leonidov A.V. Physica A 353 (2005) 388
28. NYSE data, 〈http://www.nysedata.com/〉.
29. A.C. Silva, Ph.D. Thesis, Chapter 5, University of Maryland, 2005, 〈http://arxiv.org/abs/physics/0507022〉.
30. L. Gillemot, J.D. Farmer, F. Lillo, 〈http://arxiv.org/abs/physics/0510007〉.
31. Farmer J.D., Gillemot L., Lillo F., Mike S., and Sen A. Quant. Finance 4 (2004) 383
32. Banerjee A., Yakovenko V.M., and Di Matteo T. Physica A 370 (2006) 5459
33. Drǎgulescu A., and Yakovenko V.M. Quant. Finance 2 (2002) 443
34. We are also aware that the variation of volatility during a day has the well-known U-shape, with the highest number of trades at the opening and closing times [29].
35. Madan D.B., and Seneta E. J. Bus. 63 (1990) 511