Providing a model for tail risk estimation using extreme Value mixture models (Parametric, semi-parametric and non-parametric)
Subject Areas :
Financial Knowledge of Securities Analysis
ali
soori
1
(دکترای تخصصی دانشیار دانشکده اقتصاد،دانشگاه تهران، تهران، ایران)
bahman
esmaeili
2
(Ph.D. student, Department of Finance, Accounting and Management Faculty of Tehran University)
vahid
nobakht
3
(دانشجوی دکترای مالی دانشکده مدیریت و حسابداری، دانشگاه علامه طباطبایی، تهران، ایران)
Received: 2022-01-11
Accepted : 2022-01-11
Published : 2021-11-22
Keywords:
Tail Risk,
Extreme Value,
Volatility Clustering,
Abstract :
Financial market participants are constantly exposed to uncertainty and investment risk. Predicting and calculating risk is one of the most important issues in the field of financial issues. Reviewing the financial crises of recent years, it can be inferred that one of the reasons for these crises is the excessive attention to the repetitive central data and the lack of attention to the extreme data. In other words, in the analysis of financial data, the end part of the distribution should also be considered. The purpose of this study is to provide a model for tail risk estimation using extreme value mixture models. Accordingly, four one-tailed models and one two-tailed model in two simple functions and GARCH have been used. Modeling is based on three categories of data. The studied data include total index, price index (homogeneous) and index of top 50 companies. According to the obtained results, simulation of models with GARCH significantly improves the performance of models and reduces the error rate of simulated data in GARCH-based models. The findings also indicate that two-tailed models are more accurate than one-tailed models.
References:
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Cryer, Kung-Sik. And Jonathan D. Cryer (2008). Time Series Analysis with Application in R (Second Edition). Springer Texts in Statistics. 287-392.
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Heidari, Hadi, Keshavarz, Gholamreza, (2017), Ranking of Parametric Value at Risk Models by Considering the Shareholder Trading Position (Application of Asymmetric Distribution Functions in Family Models (GARCH), Quarterly Journal of Economic Research, Volume: 17, Issue: 66. (In Persian)
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MacDonald, A. E., C. J. Scarrott, D. S. Lee, B. Darlow, M. Reale, and G. Russell (2011). A flexible extreme value mixture model. Computational Statistics and Data Analysis.
Naderi Noor Aini, Mohammad Mehdi, (2018), Selection of the optimal method of calculating the value at risk of investment funds, asset management and financing, Volume 6, Number1- Consecutive Issue 20, Spring 2018, pp -159-180. (In Persian)
Park, M.H. and Kim, J.H. (2016). Estimating extreme tail risk measures with generalized Pareto distribution. Computational Statistics and Data Analysis, 98, 91–104.
Pedro Gerhardt Gavronski, Flavio A. Ziegelmann, Measuring systemic risk via GAS models and extreme value theory: Revisiting the 2007 financial crisis, Finance Research Letters, 2020, 101498, ISSN 1544-6123.
Pickands, J. (1971). The two-dimensional Poisson process and extremal processes. Journal of Applied Probability 8(4).
Rydell, S. (2013). The use of extreme value theory and time series analysis to estimate risk measures for extreme events, Umea University. 3-13.
Zhao, X., C. J. Scarrott, L. Oxley, and M. Reale (2010). Extreme value modeling for forecasting market crisis impacts. Applied Financial Economics 20(1-2).
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آقامحمدی، احمد؛ اوحدی، فریدون؛ صیقلی، محسن؛ بنی مهد، بهمن، (1398). برآورد ریسک سرمایه‌گذاری در یک پرتفوی ارز دیجیتال و بهینه‌سازی آن با استفاده از روش ارزش در معرض خطر، فصل‌نامه علمی پژوهشی دانش مالی تحلیل اوراق بهادار، 47، 30-17.
رستمی، علی؛ نیکنیا، نرگس، (1392). تأثیر متنوع‌سازی پرتفوی بر ارزش در معرض ریسک در بورس اوراق بهادار تهران، فصل‌نامه علمی پژوهشی دانش سرمایه‌گذاری، 6 ،88-83.
رهنمای رودپشتی، فریدون؛ قندهاری، شراره، (1394). برآورد ارزش در معرض خطر مبتنی بر محدودیت بر ارزیابی عملکرد مدیریت پرتفوی فعال در بورس اوراق بهادار تهران. مهندسی مالی و مدیریت اوراق بهادار (مدیریت پرتفوی)، 6(24)، 113-91.
قالیباف اصل، حسن؛ گورداداش مهربانی، نازیال؛ دهقان نیری، لیلا (1394). بررسی رابطه میان ریسک‌گریزی مدیران و عملکرد نهادهای مالی در بازار سرمایه (مطالعه موردی صندوق‌های مشترک سرمایه‌گذاری)، راهبرد مدیریت مالی، 3 (10)، 23-1.
Antunes, R., Gonzalez, V. (2015). A Production Model for Construction: A Theoretical Framework. Buildings, 5(1), 209-228.
Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance.
Ayusuk, A. and Sriboonchitta, S., (2016) Copula Based Volatility Models and Extreme Value Theory for Portfolio Simulation with an Application to Asian Stock Markets. In Causal Inference in Econometrics, 14(2), 279-293.
Behrens, C. N., H. F. Lopes, and D. Gamerman (2004). Bayesian analysis of extreme events with threshold estimation. Statistical Modelling.
Cryer, Kung-Sik. And Jonathan D. Cryer (2008). Time Series Analysis with Application in R (Second Edition). Springer Texts in Statistics. 287-392.
Dehghan Manshadi, Samaneh, Abdolrahimian, Mohammad Hossein, (2017), Application of Differential Risk Value (IVaR), in calculating investment portfolio risk using the previous and last approach, Strategic Management Thought, Year 11, Fall and Winter 2017, No. 2. (In Persian)
Ferreira, Ana and Haan De Laurens (2015). On the Block Maxima Method in Extreme
Fisher, R. A., & Tippett, L. H. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proceeding of Cambridge Philosophical Society, 24, 180-190.
Gencay, R., & Selcuk, F. (2004). Extreme value theory and Value-at-Risk: Relative performance in emerging markets. International Journal of Forecasting, 20(2), 287-303.
Heidari, Hadi, Keshavarz, Gholamreza, (2017), Ranking of Parametric Value at Risk Models by Considering the Shareholder Trading Position (Application of Asymmetric Distribution Functions in Family Models (GARCH), Quarterly Journal of Economic Research, Volume: 17, Issue: 66. (In Persian)
Hellman, Alexandra (2015). Estimating value at Risk – an Extreme Value Approach. Stockholms University.
Hu, Yang (2013). Extreme Value Mixture Modelling with Simulation Study and Applications in Finance and Insurance.
Karmakar, M., & Paul, S. (2016). Intraday risk management in International stock markets: A conditional EVT approach. International Review of Financial Analysis, 44, 34-55.
Kausik Chaudhuri, Rituparna Sen, Zheng Tan, Testing extreme dependence in financial time series, Economic Modelling, Volume 73, 2018, Pages 378-394, ISSN 0264-9993.
Lotfalipour, Mohammad Reza, Nosrati, Mahdieh, Ghadiri Moghadam, Abolfazl, Filsarai, Mehdi. (2017). Measuring the value at risk of portfolio conditional risk by FIGARCH - EVT method in Tehran Stock Exchange. 8 (31), 281-295. (In Persian)
MacDonald, A. E., C. J. Scarrott, D. S. Lee, B. Darlow, M. Reale, and G. Russell (2011). A flexible extreme value mixture model. Computational Statistics and Data Analysis.
Naderi Noor Aini, Mohammad Mehdi, (2018), Selection of the optimal method of calculating the value at risk of investment funds, asset management and financing, Volume 6, Number1- Consecutive Issue 20, Spring 2018, pp -159-180. (In Persian)
Park, M.H. and Kim, J.H. (2016). Estimating extreme tail risk measures with generalized Pareto distribution. Computational Statistics and Data Analysis, 98, 91–104.
Pedro Gerhardt Gavronski, Flavio A. Ziegelmann, Measuring systemic risk via GAS models and extreme value theory: Revisiting the 2007 financial crisis, Finance Research Letters, 2020, 101498, ISSN 1544-6123.
Pickands, J. (1971). The two-dimensional Poisson process and extremal processes. Journal of Applied Probability 8(4).
Rydell, S. (2013). The use of extreme value theory and time series analysis to estimate risk measures for extreme events, Umea University. 3-13.
Zhao, X., C. J. Scarrott, L. Oxley, and M. Reale (2010). Extreme value modeling for forecasting market crisis impacts. Applied Financial Economics 20(1-2).
