| تعداد نشریات | 24 |
| تعداد شماره‌ها | 934 |
| تعداد مقالات | 8,383 |
| تعداد مشاهده مقاله | 16,981,645 |
| تعداد دریافت فایل اصل مقاله | 14,371,246 |
Risk Estimation for the New Heavy Tail Distribution using Bayesian Approach | ||
| Iranian Journal of Economic Studies | ||
| مقاله 6، دوره 13، شماره 1 - شماره پیاپی 25، 2024، صفحه 109-132 اصل مقاله (814.27 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijes.2025.52208.1995 | ||
| نویسندگان | ||
| Hanieh Panahi* 1؛ Showkat Ahmad Lone2؛ Hooman Aliakbarian3 | ||
| 1Department of Mathematics and Statistics, La.C., Islamic Azad University, Lahijan, Iran. | ||
| 2Department of Basic Sciences, Saudi electronic university, Riyadh, Saudi Arabia. | ||
| 3Department of financial Management, La.C., Islamic Azad University, Lahijan, Iran. | ||
| چکیده | ||
| This study addresses the evaluation of Value-at-Risk (VaR) using a Bayesian approach, specifically employing the heavy-tailed Weibull (HTW) distribution. The VaR is a crucial financial metric for business and investment decision-making. While various methods exist for estimating VaR, this research focuses on statistical techniques utilizing heavy-tail distributions. The paper extends the heavy-tailed Weibull model, which is particularly relevant for financial applications and provides reliable predictions for heavy-tailed data. The statistical properties of the HTW distribution are developed and Bayesian estimates under multiple symmetric and asymmetric loss functions are obtained. The Bayes estimate is evaluated from the posterior distribution that minimizes the corresponding posterior risk. Due to the complexity of the posterior distribution, the Metropolis-Hastings algorithm (MHA) is implemented to draw posterior samples. The Markov Chain Monte Carlo sample convergence is evaluated through diagnostic plots. The insurance loss data is used to display the application of the presented methodology in a real-world situation. The outcomes showed that Bayesian estimates can be used to evaluate the Value-at-Risk measure well. Financial institutions and risk managers can consider implementing Bayesian methods with heavy-tailed distributions, particularly the heavy-tailed Weibull model, for more accurate VaR estimation. This approach is especially valuable for portfolios with extreme events or fat-tailed return distributions. | ||
| کلیدواژه‌ها | ||
| Heavy-tailed Weibull؛ Precautionary loss function؛ Metropolis-Hastings method؛ Value-at-Risk measure | ||
| مراجع | ||
|
Alzaatreh, A., Lee, C., & Famoye F. (2013). A new method for generating families of continuous distributions. Metron, 71(1), 63–79. Asadi, A., Zare, H., Ebrahimi, M. & Piraiee, K. (2018). Sentiment Shock and Stock Price Bubbles in a Dynamic Stochastic General Equilibrium Model Framework: The Case of Iran. Iranian Journal of Economic Studies, 7(2), 115-150. Bali, T.G., (2007). A Generalized Extreme Value Approach to Financial Risk Measurement, Journal of Money, Credit and Banking, Blackwell Publishing, 39(7), 1613-1649. Benkhelifa, L., (2021a). The Weibull Birnbaum-Saunders Distribution And Its Applications. Statistics, Optimization & Information Computing, 9(1), 61-81. Benkhelifa, L. (2021b). The Beta Reduced Modified Weibull Distribution with Applications to Reliability Data. Journal of Reliability and Statistical Studies, 14, 323–352. Bebbington, M., Lai, C.D. & Zitikis, A. (2007). A flexible Weibull extension. Reliability Engineering and System Safety, 92:719-726. Chronopoulos, I., Raftapostolos , A., & Kapetanios, G. (2024). Forecasting Value-at-Risk Using Deep Neural Network Quantile Regression, Journal of Financial Econometrics, 22(3), 636–669. Chinhamu, K., Huang, C.K., Huang, C.S., & Chikobvu, D., (2015). Extreme risk, value-at-risk and expected shortfall in the gold market, International Business & Economics Research Journal, 14 (1),107–122. Riad, F, Hussam, E, Gemeay, A, Aldallal,R, &Afify, A. (2022). Classical and Bayesian inference of the weighted-exponential distribution with an application to insurance data, Mathematical Biosciences and Engineering, 19(7), 6551-6581. Lai, C.D., Xie, M., & Murthy, D.N.P., (2003). A modified Weibull distribution. IEEE Transactions on Reliability, 52(1):33-37. Luger, R., (2012). Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations, Computational Statistics & Data Analysis, 56(11), 3198-3211. Famoye, F., Lee, C. & Olumolade, O. (2005). The beta-Weibull distribution. Journal of Statistical Theory and Applications, 4(2):121-136. Ghazal, M.G.M., & Radwan, H.M.M. (2022). A reduced distribution of the modified Weibull distribution and its applications to medical and engineering data, 19, 13193-13213. Mahdavi, P. Ehsani, M.A. (2022). Dynamic Causal Effects in Econometrics with a Focus on the Nonparametric Method: A Review Paper, Iranian Journal of Economic Studies, 11(2), 427-449. Martın, J., Parra, M.I., Pizarro, M.M., & Sanjuan, E.L. (2022). Baseline methods for the parameter estimation of the generalized Pareto distribution, Entropy, 24 (2), 178. Müller, F.M., & Brutti Righi, M. (2024). Comparison of Value at Risk (VaR), Multivariate Forecast Models, 63, 75–110. Moradi, N., Panahi, H., & Habibirad, A. (2022). Estimation for the Three-Parameter Exponentiated Weibull Distribution under Progressive Censored Data, Journal of the Iranian Statistical Society, 21 (1), 153-177. Nelder, J. (1965). A simplex algorithm for function minimization. Computational Journal, 7, 308–313. Panahi, H. (2019). Value at Risk Estimation using the Kappa Distribution with Application to Insurance Data, International Journal of Finance & Managerial Accounting, 4 (14), 91-100. Panahi, H. (2025). Statistical inferences of reliability and order-restricted nano-droplet rebound by comparative Kumaraswamy populations based on balanced joint progressive censoring. Physica Scripta, 100(2), 025024. Peng, S., Yang, S., & Yao, J. (2020). Improving Value-at-Risk prediction under model uncertainty, Journal of Financial Econometrics, 7, 34-42. Socgnia, V.K., & Wilcox, D. (2014). A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns, Journal of applied Mathematics, 4, 55-72. Sarhan A.M., & Apaloo, J. (2013). Exponentiated modified Weibull extension distribution. Reliability Engineering and System Safety, 112:137-144. Spierdijk, S. (2016). Confidence intervals for ARMA–GARCH Value-at-Risk: The case of heavy tails and skewness, Computational Statistics & Data Analysis, 100, 545-559. Trzpiot, G., & Majewska, J. (2010). Estimation of value at risk: Extreme value and robust approaches. Operations Research and Decisions, 20 (1), 131–143. Vardani, M. H., Panahi, H., & Behzadi, M. H. (2024). Statistical inference for marshall-olkin bivariate Kumaraswamy distribution under adaptive progressive hybrid censored dependent competing risks data. Physica Scripta, 99(8), 085272. Zhao, W., Khosa, S.K., Ahmad, Z., Aslam, M., & Afify, A.Z. (2020). Type-I heavy tailed family with applications in medicine, engineering and insurance. PLoS ONE, 15(8): e0237462. | ||
|
آمار تعداد مشاهده مقاله: 432 تعداد دریافت فایل اصل مقاله: 414 |
||