Abstract
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.
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- 1.
The maximum of these distributions was given the name optimal investment horizon.
- 2.
In this context, using logarithmic returns makes it possible to map the inverse statistics problem onto the first passage problems of diffusion.
- 3.
- 4.
These distributions are also known as Wald distributions.
- 5.
Total return price series are series where dividends, splits, mergers, etc., have been taken into account and are included in the price series.
- 6.
The 27 countries are Argentina, Brazil, Chile, China, Colombia, Czech Republic, Egypt, Hungary, India, Indonesia, Israel, Jordan, Malaysia, Mexico, Morocco, Pakistan, Peru, Philippines, Poland, Russia, South Africa, South Korea, Sri Lanka, Taiwan, Thailand, Turkey, and Venezuela.
- 7.
The chosen countries are Australia, Belgium, Canada, Denmark, Finland, France, Germany, Ireland, Italy, Japan, Netherlands, New Zealand, Spain, Sweden, United Kingdom and United States.
- 8.
To keep the usual convention within inverse statistics one should normalize (13) by dividing by \(q + (1 - q){P}^{-}\).
- 9.
Considering the logarithmic price changes without unit, the drift, μ, is measured in units of (day− 1), while volatility, σ is measured in units of \(({\sqrt{\mathrm{days}}}^{\,-1})\).
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Ahlgren, P.T.H., Dahl, H., Jensen, M.H., Simonsen, I. (2010). What Can Be Learned from Inverse Statistics?. In: Takayasu, M., Watanabe, T., Takayasu, H. (eds) Econophysics Approaches to Large-Scale Business Data and Financial Crisis. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53853-0_13
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DOI: https://doi.org/10.1007/978-4-431-53853-0_13
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