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Rate of convergence in the framework of CLT and Risk evaluation on financial markets.

This study explores the rate of convergence in the framework of Central Limit Theorem (CLT) and its implications for risk evaluation on financial markets. It highlights the limitations of using normal distribution models and presents alternative models based on stable distributions, subordination models, mixture models, Levy processes, and more. The study also proposes a methodology for constructing G-bounds and tests the weak-form efficiency hypothesis using various statistical tests. The results provide insights into the accuracy of risk evaluation and the efficiency of stock markets.

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Rate of convergence in the framework of CLT and Risk evaluation on financial markets.

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  1. Rate of convergence in the framework of CLT and Risk evaluation onfinancial markets. Levon Kazaryan, Gregory Kantorovich Higher School of Economics Higher School of Economics Mexico, 2017 www.hse.ru

  2. Introduction In economics theory and on practice often are used models with normal distribution. But empirical researches show, that using of normal distribution on practice do not take in consideration arise of fat tails. Hence, there is alternative for models based on normal distributions such as: • Stable distributions • Clark’s subordination model • Mixture of distributions’ model • General Levy processes • Variable and stochastic volatility • Microstructural models • Various non-normal distribution models Higher School of Economics , Mexico, 2017 2/24

  3. Introduction Higher School of Economics , Mexico, 2017 3 /24

  4. Methods and methodology Methodology Innovative method of construction G- bounds by Y. Gabovich Hypotheses of weak form efficiency by E. Fama. Methods • Runs test • Random walk test • Construction of G bounds for log returns of stock market indexes Correlation The rate of convergence Test of Weak-form efficiency Higher School of Economics , Mexico, 2017 4 /24

  5. Hypothesis H0:G bounds evaluate the risk of large losses on the stock markets more accurately than the normal distribution. H1:Indexes of observable countries are efficiency in the weak form. H2:There is a negative relationship Between the Weak-form efficiency of the stock market and the risk of large losses on it. Higher School of Economics , Mexico, 2017 5 /24

  6. Definition of left tail fatness Higher School of Economics , Mexico, 2017 6 /24

  7. Berry-Esseen Theorem Higher School of Economics , Mexico, 2017 7 / 24

  8. Construction of G(n,t) tail estimates Higher School of Economics , Mexico, 2017 8 / 24

  9. Construction of G1(t) tail estimates Higher School of Economics , Mexico, 2017 9 / 24

  10. Construction of G1(t) tail estimates Higher School of Economics , Mexico, 2017 10 / 24

  11. Construction of G2(t) tail estimates Higher School of Economics , Mexico, 2017 11 / 24

  12. Refinement of G*1(t) tail estimates Higher School of Economics , Mexico, 2017 12 / 24

  13. Data Higher School of Economics , Mexico, 2017 13 /24

  14. Results of construction G bounds G bounds of S&P500 Higher School of Economics , Mexico, 2017 14 / 24

  15. Results of construction G bounds G bounds of RTSI Higher School of Economics , Mexico, 2017 15 / 24

  16. Analysis of fatness of left tail Fatness of left tail S&P500 Fatness of left tail RTSI Higher School of Economics , Mexico, 2017 16 / 24

  17. Garch Model S&P500 Higher School of Economics , Mexico, 2017 17 / 24

  18. Garch Model RTSI Higher School of Economics , Mexico, 2017 18 / 24

  19. Results of construction G*1 bound Applying the refinement for the G1-bound using the Vysochanskij–Petunin inequality for the RTSI Higher School of Economics , Mexico, 2017 19 / 24

  20. Comparison of models for the RTS index Higher School of Economics , Mexico, 2017 20 / 24

  21. Information efficiency analysis Runs test Results of testing Algorithm of testing Weak-form efficiency of stock market Random walk test Weak-form efficiency of stock market Higher School of Economics , Mexico, 2017 21 / 24

  22. Results of logit model Results of logit model testing Higher School of Economics , Mexico, 2017 22 / 24

  23. Conclusion Confirmation of H0 hypothesis H1 hypothesis was partially confirmed. Confirmation of H2 hypothesis Constructed logit model let us find a negative correlation between deviation of observed indexes log returns and weak form efficiency For log returns of observed effective stock markets in the weak form fatness ratio is less than for ineffective stock markets This area of research carries great potential for further research Higher School of Economics , Mexico, 2017 23 / 24

  24. Conclusion

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