What Can Be Learned from Inverse Statistics?
One stylized fact of financial markets is an asymmetry between the most likely time to profit and to loss. This gain–loss asymmetry is revealed by inverse statistics, a method closely related to empirically finding first passage times. Many papers have presented evidence about the asymmetry, where it appears and where it does not. Also, various interpretations and explanations for the results have been suggested. In this chapter, we review the published results and explanations. We also examine the results and show that some are at best fragile. Similarly, we discuss the suggested explanations and propose a new model based on Gaussian mixtures. Apart from explaining the gain–loss asymmetry, this model also has the potential to explain other stylized facts such as volatility clustering, fat tails, and power law behavior of returns.
KeywordsGaussian Mixture Model Stylize Fact Return Level Bond Price Geometrical Brownian Motion
- 1.Frisch U (1995) Turbulence: the legacy of A.N. Kolmogorov. Cambridge University Press, CambridgeGoogle Scholar
- 3.Doyne Farmer J (1999) Comput Sci Eng 1:26Google Scholar
- 11.Bouchaud J-P, Potters M (2000) Theory of financial risks: from statistical physics to risk management. Cambridge University Press, CambridgeGoogle Scholar
- 12.Mantegna RN, Stanley HE (2000) An introduction to econophysics: correlations and complexity in finance. Cambridge University Press, CambridgeGoogle Scholar
- 13.Donangelo R, Jensen MH, Simonsen I, Sneppen K (2006) J Stat Mech L11001:1Google Scholar
- 14.Hull J (2000) Options, futures, and other derivatives, 4th edn. Prentice-Hall, LondonGoogle Scholar
- 15.Karlin S, Taylor HM (1998) A first course in stochastic processes, 2nd edn. Academic, New YorkGoogle Scholar
- 26.Siven J, Lins J, Hansen JL (2009) J Stat Mech P02004:1Google Scholar
- 27.Balogh E, Neda Z, Nagy BZs, Simonsen I Persistent collective trend in stock markets (in preparation)Google Scholar
- 28.Lillo F, Doyne Farmer J (2004) Stud Nonlinear Dyn Econom 4:3Google Scholar