- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Relativistic statistical arbitrage

A. D. Wissner-Gross1,* and C. E. Freer2,†

  • 1The MIT Media Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *alexwg@post.harvard.edu
  • †Present address: Department of Mathematics, University of Hawai‘i at Mānoa, Honolulu, Hawai‘i 96822, USA; freer@math.mit.edu
PDF

Phys. Rev. E 82, 056104 – Published 5 November, 2010

DOI: https://doi.org/10.1103/PhysRevE.82.056104

Abstract

Recent advances in high-frequency financial trading have made light propagation delays between geographically separated exchanges relevant. Here we show that there exist optimal locations from which to coordinate the statistical arbitrage of pairs of spacelike separated securities, and calculate a representative map of such locations on Earth. Furthermore, trading local securities along chains of such intermediate locations results in a novel econophysical effect, in which the relativistic propagation of tradable information is effectively slowed or stopped by arbitrage.

View figure in article

Article Text

References (66)

  1. T. L. Bhupathi, N. Carolina J. Law Technol. 11, 377 (2010) [http://cite.ncjolt.org/11NCJLTech377].
  2. B. S. Donefer, J. Trading 5, 31 (2010).
  3. E. R. Fernholz, Stochastic Portfolio Theory (Springer, New York, 2002).
  4. E. R. Fernholz and I. Karatzas, Ann. Finance 1, 149 (2005).
  5. E. R. Fernholz and C. Maguire, Jr., Financ. Anal. J. 63, 46 (2007).
  6. C. W. J. Granger, J. Econometrics 16, 121 (1981).
  7. C. W. J. Granger and A. A. Weiss, in Studies in Econometrics: Time Series and Multivariate Statistics, edited by S. Karlin, T. Amemiya, and L. A. Goodman (Academic Press, New York, 1983), p. 255.
  8. R. F. Engle and C. W. J. Granger, Econometrica 55, 251 (1987).
  9. Y. Lin, M. McCrae, and C. Gulati, J. Appl. Math. Decis. Sci. 2006, 1 (2006).
  10. S. K. Hansda and P. Ray, Econ. Polit. Wkly. 38, 741 (2003) [http://epw.in/epw/user/loginArticleError.jsp?hid_artid=2509].
  11. M. Monoyios and L. Sarno, J. Futures Markets 22, 285 (2002).
  12. P. C. Liu and G. S. Maddala, J. Int. Money Finance 11, 366 (1992).
  13. G. Vidyamurthy, Pairs Trading: Quantitative Methods and Analysis (Wiley, New York, 2004).
  14. C. L. Dunis and R. Ho, J. Asset Manag. 6, 33 (2005).
  15. R. T. Baillie and T. Bollerslev, J. Finance 44, 167 (1989).
  16. A. W. Lo and A. C. MacKinlay, Rev. Financ. Stud. 1, 41 (1988).
  17. J. M. Poterba and L. H. Summers, J. Financ. Econ. 22, 27 (1988).
  18. S. Koumkwa and R. Susmel, J. Appl. Econ. XI, 399 (2008) [http://econpapers.repec.org/article/cemjaecon/v_3a11_3ay_3a2008_3an_3a2_3ap_3a399-425.htm].
  19. C. Doidge, G. A. Karolyi, and R. M. Stulz, J. Financ. Econ. 91, 253 (2009).
  20. L. Gagnon and G. A. Karolyi, J. Financ. Econ. 97, 53 (2010).
  21. K. F. Kroner and J. Sultan, J. Financ. Quant. Anal. 28, 535 (1993).
  22. D. S. Ehrman, The Handbook of Pairs Trading: Strategies Using Equities, Options, and Futures (Wiley, New York, 2005).
  23. O. Vasicek, J. Financ. Econ. 5, 177 (1977).
  24. G. E. Uhlenbeck and L. S. Ornstein, Phys. Rev. 36, 823 (1930).
  25. M. Kac, Am. Math. Monthly 54, 369 (1947).
  26. P. Ehrenfest and T. Ehrenfest, Z. Phys. 8, 311 (1907).
  27. J. Voit, The Statistical Mechanics of Financial Markets, 2nd ed. (Springer, New York, 2003).
  28. R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, 2nd ed. (Springer, New York, 2005).
  29. T. L. Lai and H. Xing, Statistical Models and Methods for Financial Markets (Springer, New York, 2008).
  30. J. P. Fouque, G. Papanicolaou, and K. Sircar, Derivatives in Financial Markets with Stochastic Volatility (Cambridge University Press, Cambridge, England, 2000).
  31. J. Masoliver and J. Perelló, Int. J. Theor. Appl. Finance 5, 541 (2002).
  32. S. Miccichè, G. Bonanno, F. Lillo, and R. N. Mantegna, Physica A 314, 756 (2002).
  33. J. Perelló, J. Masoliver, and J.-P. Bouchaud, Appl. Math. Finance 11, 27 (2004).
  34. N. Shephard, Stochastic Volatility: Selected Readings (Oxford University Press, Oxford, England, 2005).
  35. J. Masoliver and J. Perelló, Quant. Finance 6, 423 (2006).
  36. Z. Eisler, J. Perelló, and J. Masoliver, Phys. Rev. E 76, 056105 (2007).
  37. J. Perelló, R. Sircar, and J. Masoliver, J. Stat. Mech.: Theory Exp. (2008), P06010.
  38. G. Bormetti, V. Cazzola, G. Montagna, and O. Nicrosini, J. Stat. Mech.: Theory Exp. 2008, P11013 (2008).
  39. G. Bormetti, V. Cazzola, D. Delpini, G. Montagna, and O. Nicrosini, J. Phys.: Conf. Ser. 221, 012014 (2010).
  40. L. Z. J. Liang, D. Lemmens, and J. Tempere, Eur. Phys. J. B 75, 335 (2010).
  41. R. J. Elliott, J. Van Der Hoek, and W. P. Malcolm, Quant. Finance 5, 271 (2005).
  42. W. K. Bertram, Physica A 388, 2865 (2009).
  43. S. R. Baronyan, İ. İ. Boduroğlu, and E. Şener, Manch. Sch. 78, 114 (2010).
  44. P. C. B. Phillips and S. Ouliaris, J. Econ. Dyn. Control 12, 205 (1988).
  45. H.-L. Han and M. Ogaki, Int. Rev. Econ. Finance 6, 107 (1997).
  46. G. Elliott, M. Jansson, and E. Pesavento, J. Bus. Econ. Stat. 23, 34 (2005).
  47. P. Fortune, N. Engl. Econ. Rev. (2000), 19 [http://ideas.repec.org/a/fip/fedbne/y2000isepp19-44.html].
  48. G. J. Alexander, E. Ors, M. A. Peterson, and P. J. Seguin, J. Corp. Finance 10, 549 (2004).
  49. U. Nielsson, J. Financ. Markets 12, 229 (2009).
  50. M. Kearns, A. Kulesza, and Y. Nevmyvaka, J. Trading 5, 50 (2010).
  51. R. Fürth, Z. Phys. 2, 244 (1920).
  52. G. I. Taylor, Proc. London Math. Soc. s2-20, 196 (1922).
  53. S. Goldstein, Q. J. Mech. Appl. Math. 4, 129 (1951).
  54. M. Kac, Rocky Mountain J. Math. 4, 497 (1974).
  55. J. Masoliver, J. M. Porrà, and G. H. Weiss, Phys. Rev. E 48, 939 (1993).
  56. D. Mugnai, A. Ranfagni, R. Ruggeri, and A. Agresti, Phys. Rev. E 49, 1771 (1994).
  57. J. Masoliver and G. H. Weiss, Phys. Rev. E 49, 3852 (1994).
  58. J. Dunkel, P. Talkner, and P. Hänggi, Phys. Rev. D 75, 043001 (2007).
  59. A. Di Crescenzo and F. Pellerey, Appl. Stochastic Models Bus. Ind. 18, 171 (2002).
  60. N. Ratanov, J. Appl. Math. Stochastic Anal. 2007, 72326 (2007).
  61. N. Ratanov, Quant. Finance 7, 575 (2007).
  62. N. Ratanov and A. Melnikov, Stochastics 80, 247 (2008).
  63. V. Gerasik and M. Stastna, Phys. Rev. E 81, 056602 (2010).
  64. D. D. Joseph and L. Preziosi, Rev. Mod. Phys. 61, 41 (1989).
  65. D. D. Joseph and L. Preziosi, Rev. Mod. Phys. 62, 375 (1990).
  66. P. Young, Capital Market Revolution: The Future of Markets in an Online World (Prentice-Hall, Englewood Cliffs, NJ, 1999).

Outline

Information

Phys. Rev. E 82, 056104– Published 5 November, 2010
  • Received 29 July 2010

© 2010 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation