برآورد و ارزیابی ارزش در معرض ریسک و ریزش مورد انتظار ناپارامتریک بر مبنای تحلیل مؤلفه‌های اساسی در بورس اوراق بهادار تهران

نوع مقاله : علمی - پژوهشی

نویسندگان

دانشگاه علامه طباطبایی

چکیده

در این پژوهش، کاربرد روش شبیه‌سازی مونت‌کارلو بر مبنای تحلیل مؤلفه‌های اساسی، به‌عنوان روشی با رویکردی ناپارامتریک برای محاسبه‌ ارزش در معرض ریسک و ریزش مورد­انتظار، بررسی شده است. در این روش سعی می­شود برخی مشکلات روش شبیه‌سازی مونت‌کارلو از قبیل محاسبات زیاد و زمان‌بر­بودن آن مرتفع شود. بدین منظور با به‌کارگیری این روش، ارزش در معرض ریسک و ریزش مورد‌انتظار شاخص صنایع «بورس اوراق بهادار تهران» برآورد و نتایج به‌دست‌آمده از این روش با نتایج روش ریسک‌متریکس و شبیه‌سازی مونت‌کارلو به روش مرسوم مقایسه شد. بررسی‌های انجام‌گرفته توسط تکنیک‌های پس‌آ‌زمایی حاکی از نتایج قابل‌اتکای این روش و روش مرسوم شبیه‌سازی مونت‌کارلو و برتری این دو روش در مقایسه با روش ریسک‌متریکس است؛ همچنین بررسی زمان لازم برای محاسبه‌ ارزش در معرض ریسک و ریزش مورد­انتظار نشان­هنده سرعت بیشتر روش شبیه‌سازی مونت‌کارلو بر مبنای تحلیل مؤلفه‌های اساسی نسبت به روش مرسوم شبیه‌سازی مونت‌کارلو است.

عنوان مقاله [English]

Estimate and evaluate non-parametric value at risk and expected shortfall based on principal component analysis in Tehran Stock Exchange

نویسندگان [English]

  • Mohammad Hashem Botshekan
  • Moslem Peymani
  • Mohammad Masoud Sadredin Karami
Allame Tabatabaie University
چکیده [English]

In this research, the application of Monte Carlo simulation based Principal component analysis (PCA), as a nonparametric approach for calculating value at risk and expected shortfall, has been studied. This method tries to overcome some problems of conventional Monte Carlo simulation method such as excessive and time consuming calculation,. In this order, by applying Monte Carlo simulation based PCA method, we calculate VaR and ES for Tehran Stock Exchange industrial indices and compare its results with the results obtained by riskmetrics method and conventional Monte Carlo simulation method. Results from backtesting technics show Monte Carlo simulation based PCA and conventional Monte Carlo simulation method both have the same accuracy in estimating VaR and ES, but riskmetrics could not estimate VaR and ES as well like last methods. Also, assessing time needed for estimating VaR and ES shows Monte Carlo simulation based PCA a quicker method than conventional Monte Carlo simulation.

کلیدواژه‌ها [English]

  • Principal component analysis-Value at risk-Expected shortfall-Monte Carlo simulation

مراجع

  1. Adabifiroozjani, B., Mehrara, M. & Mohamadi, Sh. (2015). Estimating and evaluating VaR of Tehran Stock Exchange based on window simulation method. Journal of Economic Modeling Research, 23, 35-73 (In Persian).
  2. Adabifiroozjani, B., Mehrara, M. & Mohamadi, Sh. (2016). Forcasting and evaluating on step forward VaR of Tehran Stock Exchange by Markov Chain Monte Carlo. Financial engineering and portfolio management, 26, 101-122 (In Persian).
  3. Antonelli, S. Gabriella Iovino, M. (2002). Optimization of Monte Carlo Procedures for Value at Risk Estimates. Economic Notes by Banca Monte dei Paschi di Siena SpA, 31, 59-78.
  4. Artzner, P, Delbaen, F. Eber, J. M. & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203-28.
  5. Baek, Seungho, Cursio, Joseph D. & Cha, Seung Y. (2015). Nonparametric Factor Analytic Risk Measurement in Common Stocks in Financial Firms: Evidence from Korean Firms. Asia-Paciï‌c Journal of Financial Studies, 44, 497-536.
  6. Christoffersen, P. (1998). Evaluating Interval Forecasts. International. Economic Review, 39, 841-862.
  7. Cont, Rama, Tankov, Peter (2010). Encyclopedia of quantitative finance. Hoboken, N.J.‏‫‭: Wiley.â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌â€‌
  8. Emmer, Susanne, Kratz, Marie & Tasche, Dirk (2015). What is the best risk measure in practice? A comparison of standard measures. Journal of Risk, 18(2), 31-60.
  9. Frye, J. (1997). Principals of risk: Finding value-at-risk through factor-based interest rate scenarios. NationsBanc-CRT, April.
  10. Haas, M. (2001). New Methods in Backtesting. Financial Engineering, Research Center Caesar, Bonn.
  11. Hanifi, F. (2001). Investigating the level of risk taking of listed company in Tehran Stock Exchange via VaR. PhD’s Thesis, University of Islamic Azad Science and research brand, Tehran, Iran (In Persian).
  12. J.P. Morgan (1996). Riskmetrics, Technical Document, 4th ed., J.P. Morgan, New York.
  13. Jamshidian, F., & Zhu, Y. (1997). Scenario simulation: Theory and methodology. Finance and Stochastics, 1, 43-67.
  14. Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and psychological measurement, 20(1), 141-151.
  15. Kupiec, P. (1995). Techniques for Verifying the Accuracy of Risk Management Models. Journal of Derivatives, 3, 73-84.
  16. Mohades, F. (2010). Principal component analysis and factor analysis, case study: extracting the asset price index and its effect on inflation. Economic Research Collection of the Central Bank of the Islamic Republic of Iran, 41, 1-43 (In Persian).
  17. Mohammadian Amiri, E., Ebrahimi, S. B. & Nezhad Afrasiabi, M. (2017). Proposition of a model For Forecasting Value at Risk in One Step Ahead. Financial Engineering and Portfolio Management, 8(32), 207-220 (In Persian).
  18. Molaie, M., Sheykh, M. J. & Khodamoradi, S. (2011). Optimization of Markowitz risk management patterns, value at risk and Parametric conditional value at risk using local and global algorithms in Tehran Stock Exchange. Journal of Financial Management Perspective, 1(1), 67-95 (In Persian).
  19. O'Rourke, N., Psych, R., & Hatcher, L. (2013). A step-by-step approach to using SAS for factor analysis and structural equation modeling. Sas Institute.
  20. Peymani, M. (2015). Modeling Tehran stock exchange total index by stochastic differential equation. PhD’s Thesis, University of Allame Tabatabaie, Tehran, Iran (In Persian).
  21. Radpoor, M. & Abde Tabrizi, H. (2009). Evaluating and managing market risk. Tehran, Iran: Agah pishbord (In Persian).
  22. Raie, R, & Falahtalab, H. (2013). Application of Monte Carlo simulation and random walk process in predicting of VaR. Financial engineering and portfolio management, 16, 75-92 (In Persian).
  23. Reris, R. (2015). Principal Component Analysis and Optimization: A Tutorial. 14th INFORMS Computing Society Conference, (pp. 212-225). Richmond, Virginia.
  24. Rostami, A., Rostami, M. R., Chavoshi, K. & Niknia, N. (2015). Investigating the effect of portfolio diversification on undesirable risk in Tehran Stock Exchange. Journal of Financial Management Perspective, 5(12), 109-133 (In Persian).
  25. Sadaabadi, M. (2013). A comparative study of the efficiency of parametric and nonparametric methods for measuring the value at risk of Tehran Stock Exchange indices. Master’s Thesis, University of Economic Scienc, Tehran, Iran (In Persian).
  26. Sadeghi, M., Soroosh, A. & Farahanian, M. j. (2010). Investigating the Volatility, Favorable Risk and Unfavorable Risk in Capital Pricing Model: Evidence from Tehran Stock Exchange. Financial studies, 29, 59-78 (In Persian).
  27. Sheykhi, Z. (2010). Evaluation of Monte Carlo simulation model and RiskMetrics model in predicting market risk in Tehran Stock Exchange. Master’s Thesis, University of Islamic Aza, Tehran, Iran (In Persian).
  28. Shlens, J. (2014). A tutorial on principal component analysis. arXiv preprint arXiv:1404.1100.
  29. Taieby Sani, E., Changi Ashtiani, M. (2018). Forecasting Volatility & Risk Management in Tehran Stock Exchange through Long memory impacts. Financial Engineering and Portfolio Management, 9(34), 121-142 (In Persian).
  30. Tsay, R. S. (2014). An introduction to analysis of financial data with R. John Wiley & Sons.
  31. Yoosefi, M. & Rezghi, M. (2016). Non-negative matrix factorization: A method for analyzing unfair data. Journal of Mathematics Culture and Thought, 51, 71-90 (In Persian).
  32. Zhang, H. G., Su, C. W., Song, Y., Qiu, S., Xiao, R., & Su, F. (2017). Calculating Value-at-Risk for high-dimensional time series using a nonlinear random mapping model. Economic Modelling, 67, 355-367.
  33. Zoia, M. G., Biffi, P., & Nicolussi, F. (2018). Value at Risk and Expected Shortfall based on Gram-Charlier-like expansions. Journal of Banking & Finance, 93, 92-104.

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