Ước lượng VaR và CVaR dạng hỗn hợp các phân phối xác suất thông qua mô phỏng Monte Carlo và ứng dụng trong phân tích giá chứng khoán Việt Nam
DOI:
https://doi.org/10.24311/jabes/2018.29.9.1331Keywords:
Value at Risk (VaR) estimation, Conditional Value at Risk (CVaR) estimation, Monte Carlo simulation method, Mixture of probability distributions, Stock priceAbstract
VaR and CVaR are of great concern in risk measurement field applying for financial data. However, studies only stopped at the formula based on an approximation of data through a probability distribution, while the distribution of real data is usually a mixture of probability distributions. Therefore, it is necessary to study the VaR and CVaR estimating in the case of a mixture of probability distributions. Furthermore, the estimations also require short computational time so the author prefers to use the Monte Carlo simulation method. The author proposes the VaR and CVaR calculations in the case of probability distributions that are mixed by calibrating the Monte Carlo simulation method to suit a mixture of probability distributions. In addition, the author illustrates in cases where the simulation is known to distribute the probability of the component as well as the unknown case of the probability distribution of the component via the real data of the closing price of the Vietnam stock by a mixture of probability distributions. The algorithm-based estimation results that the author recommends is evaluated by the tail probability as well as standard deviation.
References
Acerbi, C., & Tasche, D. (2002). Expected shortfall: A natural coherent alternative to value at risk. Economic Notes, 31(2), 379–388.
Adams, Z., Füss, R., & Gropp, R. (2014). Spillover effects among financial institutions: A state–dependent sensitivity value–at–risk approach. Journal of Financial and Quantitative Analysis, 49(3), 575–598.
Belles‐Sampera, J., Guillén, M., & Santolino, M. (2014). Beyond value‐at‐risk: GlueVaR distortion risk measures. Risk Analysis, 34(1), 121–134.
Berkowitz, J., & O'Brien, J. (2002). How accurate are value‐at‐risk models at commercial banks?. The Journal of Finance, 57(3), 1093–1111.
Demir, I., Muthuswamy, J., & Walter, T. (2004). Momentum returns in Australian equities: The influences of size, risk, liquidity and return computation. Pacific-Basin Finance Journal, 12(2), 143–158.
Dietz, S., Bowen, A., Dixon, C., & Gradwell, P. (2016). ‘Climate value at risk’of global financial assets. Nature Climate Change, 6(7), 676.
Duffie, D., & Pan, J. (1997). An overview of value at risk. Journal of derivatives, 4(3), 7–49.
Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional autoregressive value at risk by regression quantiles. Journal of Business & Economic Statistics, 22(4), 367–381.
Hall, P. (1990). Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems. Journal of Multivariate Analysis, 32(2), 177–203.
Hendricks, D. (1997). Evaluation of value–at–risk models using historical data. Economic Policy Review, 2(1), 39–69.
Hennig, P., Stern, D., Herbrich, R., & Graepel, T. (2012). Kernel topic models. In Artificial Intelligence and Statistics, (pp. 511–519).
Huang, Y., Zheng, Q. P., & Wang, J. (2014). Two–stage stochastic unit commitment model including non–generation resources with conditional value–at–risk constraints. Electric Power Systems Research, 116, 427–438.
Jorion, P. (1996). Risk2: Measuring the risk in value at risk. Financial Analysts Journal, 52(6), 47–56.
Jorion, P. (2001). Value at Risk: The New Benchmark for Managing Financial Risk (3rd ed.). NY: McGraw-Hill Professional.
Krokhmal, P., Palmquist, J., & Uryasev, S. (2002). Portfolio optimization with conditional value–at–risk objective and constraints. Journal of Risk, 4, 43–68.
Lê Thanh Hoa, Phạm Hoàng Uyên, & Nguyễn Đình Thiên. (2017). Một phương pháp mới tìm khoảng mật độ hậu nghiệm cao nhất và ứng dụng. Tạp chí Phát triển Kinh tế, 28(10), 79–120.
Martins-Filho, C., Yao, F., & Torero, M. (2018). Nonparametric estimation of conditional value–at–risk and expected shortfall based on extreme value theory. Econometric Theory, 34(1), 23–67.
Pflug, G. C. (2000). Some remarks on the value-at-risk and the conditional value-at-risk. In Probabilistic Constrained Optimization (pp. 272–281). Springer, Boston, MA.
Robert, C. P. (2004). Monte Carlo Methods. John Wiley & Sons, Ltd.
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2(3), 21–42.
Rockafellar, R. T., & Uryasev, S. (2002). Conditional value–at–risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443–1471.
Rockafellar, R. T., Royset, J. O., & Miranda, S. I. (2014). Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value–at–risk. European Journal of Operational Research, 234(1), 140–154.
Zhao, H., & Luo, Y. (2018). An O (N) Sorting Algorithm: Machine Learning Sorting. arXiv preprint arXiv:1805.04272.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 JOURNAL OF ASIAN BUSINESS AND ECONOMIC STUDIES
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
