A Review of Quantitative Methods for Uncertainty in Financial Markets

DOI: https://doi.org/10.62517/jse.202511507

Author(s)

Yan Qizhen

Affiliation(s)

Hangzhou Renhe Experimental School, Zhejiang, China

Abstract

In volatile financial markets, the exclusive reliance on point forecasts proves inadequate for representing the complexity and uncertainty of future dynamics. To address this limitation and enhance the reliability of risk assessment and decision-making, the literature has advanced a broad spectrum of uncertainty quantification methodologies, incorporating both traditional statistical inference and contemporary machine learning approaches. This paper mainly reviews the machine learning and statistical methods commonly used in financial risk prediction: for example, prediction interval estimation of ensemble learning methods such as random forest; Traditional confidence interval construction and bootstrap method; Bayesian regression (such as BART) and posterior prediction based on MCMC; Application of Monte Carlo simulation in risk measurement. We discuss from the perspective of method theory and literature application, without involving specific empirical results. Finally, the advantages, disadvantages and future development directions of these methods are compared and analyzed.

Keywords

Uncertainty Quantification; Random Forest; Confidence Interval; Bayesian Regression; Monte Carlo Simulation

References

[1] Wager, S., Hastie, T., Efron, B. (2014) Confidence intervals for random forests: The jackknife and the infinitesimal jackknife. Journal of Machine Learning Research, 15(1): 1625–1651. [2] Mentch, L., Hooker, G. (2016) Quantifying uncertainty in random forests via confidence intervals and hypothesis tests. Journal of Machine Learning Research, 17(26): 1–41. [3] Efron, B., Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman & Hall, New York. [4] Johannes, M., Polson, N. (2010) MCMC methods for continuous-time financial econometrics. In: Andersen, T. G. (Ed.), Handbook of Financial Econometrics: Applications. Elsevier, Amsterdam. pp. 1–72. [5] Glasserman, P. (2003) Monte Carlo Methods in Financial Engineering. Springer, New York. [6] Hastie, T., Tibshirani, R., Friedman, J. (2009) Random forests. In: Hastie, T., Tibshirani, R., Friedman, J., (Eds.), The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York. pp. 587–604. [7] Rasmussen, C. E., Williams, C. K. I. (2006) Gaussian Processes for Machine Learning. MIT Press, Cambridge. [8] Wang, B., Li, T., Yan, Z., Zhang, G., Lu, J. (2020) Deeppipe: A distribution-free uncertainty quantification approach for time series forecasting. Neurocomputing, 397: 11–19. [9] Martin, G., Frazier, D., Maneesoonthorn, W., Loaiza-Maya, R., Huber, F., Koop, G., Maheu, J., Nibbering, D., Panagiotelis, A. (2023) Bayesian forecasting in economics and finance: A modern review. International Journal of Forecasting, 39(4): 1275–1312. [10] Lim, B., Zohren, S. (2021) Time-series forecasting with deep learning: A survey. Philosophical Transactions of the Royal Society A, 379(2194): 20200209. [11] Johansson, U., Bostrom, H., Lofstrom, T. H. (2014) Regression conformal prediction with random forests. Machine Learning, 97(1–2): 155–176. [12] Meinshausen, N., Ridgeway, G. (2006) Quantile regression forests. Journal of Machine Learning Research, 7(6): 983-999. [13] Gostkowski, M., Gajowniczek, K. (2020) Weighted quantile regression forests for bimodal distribution modeling: A loss given default case. Entropy, 22(5): 545. [14] Zou, H., Yuan, M. (2008) Composite quantile regression and the oracle model selection theory. Annals of Statistics, 36(3): 1108–1126. [15] Lian, H., Zhao, W., Ma, Y. (2019) Multiple quantile modeling via reduced-rank regression. Statistica Sinica, 29(3): 1439-1464. [16] Hao, L., Naiman, D. (2007) Quantile Regression. Sage, London. [17] Gal, Y., Ghahramani, Z. (2016) Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. International Conference on Machine Learning (ICML), 1050–1059. [18] Jang, H., Lee, J. (2017) An empirical study on modeling and prediction of bitcoin prices with Bayesian neural networks based on blockchain information. IEEE Access, 6: 5427–5437. [19] Chandra, R., He, Y. (2021) Bayesian neural networks for stock price forecasting before and during covid-19 pandemic. PLOS ONE, 16(7): e0253217. [20] Lim, B., Zohren, S. (2021) Machine learning for financial time-series forecasting: Recent advances and future challenges. Quantitative Finance, 21(9): 1411–1432. [21] Koenker, R. (2017) Quantile regression: 40 years on. Annual Review of Economics, 9: 155–176. [22] Castillo, I., Rockova, V. (2021) Uncertainty quantification for Bayesian CART. 3482-3509. [23] Fan, J., Li, Y., Zhang, C. (2023) Statistical methods for high-dimensional financial econometrics. Annual Review of Statistics and Its Application, 10: 1–26. [24] Zhang, C., Li, J., Wang, Q. (2021) Parallelized Monte Carlo methods for large-scale financial simulations. Journal of Computational Finance, 25(2): 1-28. [25] Tecdat. (2022), the Monte Carlo Monte Carlo simulation of the portfolio value at risk (VaR). https://cloud.tencent.com/developer/article/1951564