Behavioral data-driven analysis with Bayesian method for risk management of financial services

https://doi.org/10.1016/j.ijpe.2020.107737Get rights and content

Abstract

Time-varying behavioral features and non-linear dependence are widely observed in big data and challenge the operating systems and processes of risk management in financial services. In order to improve the operational accuracy of risk measures and incorporate customer behavior analytics, we propose a Bayesian approach to efficiently estimate the multivariate risk measures in a dynamic framework. The proposed method can carry the prior information into the Bayesian analysis and fully describe the risk measures’ behavior after utilizing the Cornish–Fisher (CF) approximation with Markov Chain Monte Carlo (MCMC) sampling. Therefore, the operating systems and processes of risk management can be well performed either based on the first four conditional moments of the underlying model employed to consider some specific behavioral features (e.g., the time-varying conditional multivariate skewness) or the characteristics extracted from the big data. We conduct a simulation study to distinguish the applications of CF approximation and MCMC sampling after comparing them with the classic likelihood based method. We then provide a robust procedure for empirical investigation by using the real data of U.S. DJIA stocks. Both simulation and empirical results confirm that the Bayesian method can significantly improve the operations of risk management.

Introduction

The research paradigm of operations management for financial services attempts to establish efficient operating systems and processes (OSaP) with the ubiquitous big data in financial markets, which requires convenience by reducing the formalities and links as much as possible without being limited by time and location (e.g., the 3As: any time, anywhere, any way). Financial services industry is a highly information-intensive industry. The development of information and communication technologies (e.g., big data technology) has increased the efficiency of information gathering, processing and analysis, enabling financial market participants to measure and manage risk in their OSaP more efficiently (see Oliva, 2016 for example).

Financial crisis highlighted the importance of risk measures1 for assets that are highly correlated since bounded rationality does not enable consumers to diversify risk effectively, see Abreu and Brunnermeier, 2003, Matsushima, 2013, and Guo et al. (2017) for example. When there exists systemic risk (see Lin et al. (2016)) high dimensionality particularly challenges the gauge of risk measures for portfolios of multivariate assets whose mean, volatility, and correlation evolve over time.

Oracle conducted a quantitative survey of 117 senior Finance, Risk and Data executives in the APAC region as well as 50 executives surveyed in the USA and Europe between November 2018 and January 2019.2 It examines how banks can use data to develop unified finance and risk solutions to drive innovation, operational excellence, and productivity. Existing approaches calibrate data to the parameterized probability model, and then express VaR as a function of that parameter. This indirect approach raises model misspecification bias or estimation inefficiency in high dimensionality. Collinearity is unavoidable in high dimensionality and many methods (e.g., lasso) tend to smooth away the highly collinear variables, and hence include correlated covariates in the model. Bayesian method allows a correlation-adaptive prior that lets the data itself weigh in on how collinearity to be handled. Since Bayesian approach can ideally update information with accuracy and coherency (see Hahn et al. (2018); Segnon and Trede (2018)), varieties of priors for choosing model parameters and developing model space will lead to promising selection properties see, Hosseini and Ivanov, 2019, Hosseini et al., 2019b and Hosseini et al. (2019a). In this paper, we propose a new online sequential Bayesian modeling framework that enables us to incorporate scalable data analytic and apply efficient computation (e.g., stochastic search approach) for the posterior distribution over the model space in the risk management of financial service’s OSaP.

One generally observed fact of market behavior, especially when sampling at higher frequencies, is that assets’ returns display fat tails and skewness. The skewed distribution and its extensions have been used recently in different areas; see, Zhu and Galbraith, 2010, Bernardi et al., 2012, Eling, 2014, Wu et al., 2015 and Farias et al. (2016), for example. However, Kollo (2008) point out the problems of parameter estimation produces for these distributions, and argue that the maximum likelihood method (MLE) cannot be applied without expressing the underlying density explicitly. MLE can give incorrect answers when the problem of singularity or multiple local maximum occurs, see Hamilton (1991). Discarding time-invariance as a modeling assumption (see Sun et al. (2009)) makes uncertainty about parameters, models, and forecasts accessible and irreducible in a way that standard statistical risk measurements do not. The constructive alternative offered here under the slogan Bayesian Risk Management is an online sequential Bayesian modeling framework that acknowledges all of these sources of uncertainty, without giving up the structure afforded by parametric risk models and asset-pricing models.

Value at Risk (VaR) and expected shortfall (ES) are important risk measures and applied in operations management (see Koenig and Meissner, 2015, Yau et al., 2011 among others). Measuring VaR or ES accurately remains challenging, particularly, for heterogeneous trading behavior over time. One generally observed fact of market behavior, especially when sampling at higher frequencies, is that assets’ returns display fat tails and skewness. The skewed distribution and its extensions have been used recently in different areas; see, Zhu and Galbraith, 2010, Bernardi et al., 2012, Eling, 2014, Wu et al., 2015 and Farias et al. (2016), for example. However, Kollo (2008) point out the problems of parameter estimation produces for these distributions, and argue that the maximum likelihood method (MLE) cannot be applied without expressing the underlying density explicitly. MLE can give incorrect answers when the problem of singularity or multiple local maximum occurs, see Hamilton (1991).

Thus, Bayesian methods turn to be a promising approach of statistical inference, particularly for complicated models to describe heterogeneous market behavior. Several studies have illustrated the advantages of applying Bayesian methods in operations management, for example, Boutselis and McNaught (2019) apply Bayesian networks in spare parts demand forecasting. Hosseini and Barker (2016) proposes a Bayesian network to provide a resilience-based supplier selection. Qazi et al. (2018) develops a supply chain risk network management process based on the Bayesian belief framework. Ojha et al. (2018) employ Bayesian network modeling for improved supply chain risk management. Maiyar et al. (2019) employ a Bayesian Network structure learning model to identify the relationship between product attributes and customer preferences. Kou et al. (2017) use the Bayesian MCMC method to estimate the affine jump–diffusion models. Naderkhani and Makis (2016) and Li et al. (2018) develop a multivariate Bayesian quality control chart and Zhou et al. (2017) propose a Bayesian approach to hazard rate models that reduces the need for extensive warranty claim history. In this paper, we consider a Bayesian approach to perform statistical inference for risk measures with big (high-frequency and high-dimensional) data.3

Assessing behavioral uncertainty of risk measures allows investors or risk managers to make more informed decisions. The main source of uncertainty that influences operational accuracy is the parameter uncertainty of the underlying model used to describe the dynamics of investors’ behavior, see Cairns, 2000, Barrieu and Scandolo, 2015 and Fröhlich and Weng (2018) for example. The Bayesian approach can deal with this problem efficiently by identifying the kernel characterization of the parameter uncertainty contained in the joint posterior distribution (see Lin et al. (2012), for example). This posterior distribution is clearly a probability distribution on parameter values, given the actually observed data. Therefore, a major advantage of the Bayesian approach is that the posterior distribution can be directly explained and understood. In addition, there are more advantages of using Bayesian analysis: first, the likelihood surface is often non regular and maximum likelihood estimates (MLE) tend to be unstable under a non-Gaussian distribution but Bayesian method can overcome it (Liseo and Parisi, 2013, Parisi and Liseo, 2018); second, the Bayesian approach provides the flexibility that enable the OSaP to adjust the risk measures according to subjective/empirical views.

In the intraday VaR and/or ES literature, few studies account for the risk assessment using Bayesian inference for high-dimensional dependent assets. Therefore, in this paper we investigate a portfolio of several assets with an unknown dynamic correlation structure observed frequently (i.e., every hour) and employ an appropriate Bayesian methodology to estimate the risk measures. We focus on the estimation of VaR and ES with tail dependence by the use of a Bayesian method for the portfolio risks. The main advantage of our approach is that all unknown parameters of the chosen model (for risky return) are able to be estimated simultaneously, as well as their restrictions. In addition, the VaR models with a skewed multivariate distribution allow time-varying dependence and other major features empirically observed in financial asset data, such as skewness, volatility clustering, leverage effects, and time-varying covariance. When forecasting the portfolio risk, our method obtains the forecasts by simulating from the predictive density and estimating the VaR and/or ES from empirical percentiles.

Our major contributions are summarized as follows. First, in order to capture the realistic behavioral features in big data, we adopt the multivariate GARCH models with skewed distributions for time-varying dependence. Based on these models, an efficient Bayesian procedure is proposed to estimate the multivariate VaR and/or ES such that the prior information is included in Bayesian inference. Using the Cornish–Fisher approximation of VaR during MCMC sampling can efficiently estimate risk measures. Second, we show that the dynamic correlation exhibits important influences on estimating the relevant parameters and forecasting the risk measures due to the time-varying dependence. Our simulation results confirm that the proposed Bayesian approach is exceptionally good for modeling. Third, our framework considers different behavioral features when utilizing a loss function to demonstrate the efficient risk measures for the large scale portfolio. The empirical results show that the risk forecasting of using multivariate time-varying volatility models with skewed distributions performs well after backtesting the robustness.

The rest of the paper is organized as follows. Section 2 introduces the multivariate volatility models and assumptions we adopted in the proposed Bayesian framework. Section 3 outlines the Bayesian methodology for inference, derives posterior distributions for model parameters for Bayesian inference, and discusses the computation of Multivariate Value-at-Risk (MVaR) and Multivariate Expected Shortfall (MES) estimates under the Bayesian framework. Section 4 illustrates the possible implementations of the Bayesian approach by conducting simulations. Section 5 demonstrates an empirical investigation of estimating MVaR and MES for the multivariate volatility model with skewed multivariate normal innovations by evaluating portfolio risk of U.S. DJIA stocks. Section 6 concludes.

Section snippets

Dependent assets with skewed distributions

Dynamic conditional correlation methods have been proposed by Engle (2002) to parameterize the conditional correlations directly by using the two-steps estimation, see also Tse and Tsui (2002) and Engle (2009). In this study we construct a Bayesian approach in a dynamic conditional correlation (DCC) framework with specific assumptions on the volatility dynamics, time-varying correlation, and two multivariate skewed distributions simultaneously.

Bayesian inference

Classic methods used for risk management only produce a point estimate of the financial positions but do not account for additional information of the uncertainty inherent in all estimation procedures such as confidence intervals, see Gandy and Veraart (2016), for example. Without considering the whole information of the dynamics of underlying assets turns to be problematic when a decision maker derive risk measures on portfolio of high-dimensional dependent assets. Bayesian methods are

Simulation study

Following Chen et al. (2020), we conduct a simulation study to illustrate the effectiveness and computational properties of the proposed Bayesian approach.

The motivation behind this simulation study is threefold. First, we shall verify the performance of the proposed method with the portfolio that includes dependent assets of time-varying volatility. Second, we verify the performance of the proposed method for the aggregated risk of portfolio return which is a challenging problem in practice.

Data

In this section, we perform the proposed Bayesian method for computing risk measures with the high-frequency data of ten U.S. DJIA component stocks sampled from the Trade and Quote (TAQ) database 8 from January to October 2010, see Sun et al. (2015). Our sample contains all transactions reported during the consolidated tapes hours of operation (8:00 am to 6:30 pm EST). Following 

Conclusion

In this paper, we develop a Bayesian approach for risk management that is particularly for a time-varying behavioral features and distinguish two computational cases for the proposed Bayesian method: the Cornish–Fisher approximation and MCMC. We discuss the advantages of the proposed method such as consistent measurement, computational efficiency, and compatibility. Based on these theoretic properties, we conduct both simulation and empirical study to illustrate the performance of the proposed

CRediT authorship contribution statement

Edward M.H. Lin: Formal analysis, Methodology, Software, Writing - Original Draft. Edward W. Sun: Conceptualization, Formal analysis, Methodology, Validation, Writing - Original Draft . Min-Teh Yu: Data curation, Funding acquisition, Investigation, Project administration, Resources, Writing - review & editing.

Acknowledgments

This work was financially supported by the Ministry of Science and Technology (MOST) in Taiwan. Lin was supported in part by the MOST under Grant 108-2118-M-029-006. Sun was supported by the research project funded by InfoTech Frankfurt am Main, Germany under USt-IdNr. DE320245686.

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