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33 pages, 2751 KiB

Open AccessArticle

Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations

by Takaaki Koike and Marius Hofert

Risks 2020, 8(1), 6; https://doi.org/10.3390/risks8010006 - 15 Jan 2020

Cited by 10 | Viewed by 6253

Abstract

In this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the [...] Read more.

In this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo (MC) methods often provide inefficient estimates due to the rare-event character of the crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as the Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. The efficiency of the MCMC estimators is demonstrated in a series of numerical experiments. Full article

(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)

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16 pages, 530 KiB

Open AccessArticle

Developing an Impairment Loss Given Default Model Using Weighted Logistic Regression Illustrated on a Secured Retail Bank Portfolio

by Douw Gerbrand Breed, Tanja Verster, Willem D. Schutte and Naeem Siddiqi

Risks 2019, 7(4), 123; https://doi.org/10.3390/risks7040123 - 13 Dec 2019

Cited by 5 | Viewed by 9408

Abstract

This paper proposes a new method to model loss given default (LGD) for IFRS 9 purposes. We develop two models for the purposes of this paper—LGD1 and LGD2. The LGD1 model is applied to the non-default (performing) accounts and its empirical value based [...] Read more.

This paper proposes a new method to model loss given default (LGD) for IFRS 9 purposes. We develop two models for the purposes of this paper—LGD1 and LGD2. The LGD1 model is applied to the non-default (performing) accounts and its empirical value based on a specified reference period using a lookup table. We also segment this across the most important variables to obtain a more granular estimate. The LGD2 model is applied to defaulted accounts and we estimate the model by means of an exposure weighted logistic regression. This newly developed LGD model is tested on a secured retail portfolio from a bank. We compare this weighted logistic regression (WLR) (under the assumption of independence) with generalised estimating equations (GEEs) to test the effects of disregarding the dependence among the repeated observations per account. When disregarding this dependence in the application of WLR, the standard errors of the parameter estimates are underestimated. However, the practical effect of this implementation in terms of model accuracy is found to be negligible. The main advantage of the newly developed methodology is the simplicity of this well-known approach, namely logistic regression of binned variables, resulting in a scorecard format. Full article

(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)

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15 pages, 1042 KiB

Open AccessArticle

On Identifying the Systemically Important Tunisian Banks: An Empirical Approach Based on the △CoVaR Measures

by Wided Khiari and Salim Ben Sassi

Risks 2019, 7(4), 122; https://doi.org/10.3390/risks7040122 - 12 Dec 2019

Cited by 8 | Viewed by 4051

Abstract

The aim of this work is to assess systemic risk of Tunisian listed banks. The goal is to identify the institutions that contribute the most to systemic risk and that are most exposed to it. We use the CoVaR that considered the systemic [...] Read more.

The aim of this work is to assess systemic risk of Tunisian listed banks. The goal is to identify the institutions that contribute the most to systemic risk and that are most exposed to it. We use the CoVaR that considered the systemic risk as the value at risk (VaR) of a financial institution conditioned on the VaR of another institution. Thus, if the CoVaR increases with respect to the VaR, the spillover risk also increases among the institutions. The difference between these measurements is termed △CoVaR, and it allows for estimating the exposure and contribution of each bank to systemic risk. Results allow classifying Tunisian banks in terms of systemic risk involvement. They show that public banks occupy the top places, followed by the two largest private banks in Tunisia. These five banks are the main systemic players in the Tunisian banking sector. It seems that they are the least sensitive to the financial difficulties of existing banks and the most important contributors to the distress of the other banks. This work aims to add a broader perspective to the micro prudential application of regulation, including contagion, proposing a macro prudential vision and strengthening of regulatory policy. Supervisors could impose close supervision for institutions considered as potentially systemic banks. Furthermore, regulations should consider the systemic contribution when defining risk requirements to minimize the consequences of possible herd behavior. Full article

(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)

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20 pages, 2048 KiB

Open AccessArticle

Target Matrix Estimators in Risk-Based Portfolios

by Marco Neffelli

Risks 2018, 6(4), 125; https://doi.org/10.3390/risks6040125 - 5 Nov 2018

Cited by 4 | Viewed by 3867

Abstract

Portfolio weights solely based on risk avoid estimation errors from the sample mean, but they are still affected from the misspecification in the sample covariance matrix. To solve this problem, we shrink the covariance matrix towards the Identity, the Variance Identity, the Single-index [...] Read more.

Portfolio weights solely based on risk avoid estimation errors from the sample mean, but they are still affected from the misspecification in the sample covariance matrix. To solve this problem, we shrink the covariance matrix towards the Identity, the Variance Identity, the Single-index model, the Common Covariance, the Constant Correlation, and the Exponential Weighted Moving Average target matrices. Using an extensive Monte Carlo simulation, we offer a comparative study of these target estimators, testing their ability in reproducing the true portfolio weights. We control for the dataset dimensionality and the shrinkage intensity in the Minimum Variance (MV), Inverse Volatility (IV), Equal-Risk-Contribution (ERC), and Maximum Diversification (MD) portfolios. We find out that the Identity and Variance Identity have very good statistical properties, also being well conditioned in high-dimensional datasets. In addition, these two models are the best target towards which to shrink: they minimise the misspecification in risk-based portfolio weights, generating estimates very close to the population values. Overall, shrinking the sample covariance matrix helps to reduce weight misspecification, especially in the Minimum Variance and the Maximum Diversification portfolios. The Inverse Volatility and the Equal-Risk-Contribution portfolios are less sensitive to covariance misspecification and so benefit less from shrinkage. Full article

(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)

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31 pages, 3269 KiB

Open AccessArticle

A General Framework for Portfolio Theory. Part II: Drawdown Risk Measures

by Stanislaus Maier-Paape and Qiji Jim Zhu

Risks 2018, 6(3), 76; https://doi.org/10.3390/risks6030076 - 7 Aug 2018

Cited by 8 | Viewed by 4658

Abstract

The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu (2018), presented in Part I of this series. As an alternative to classical portfolio [...] Read more.

The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu (2018), presented in Part I of this series. As an alternative to classical portfolio risk measures such as the standard deviation, we, in particular, construct risk measures related to the “current” drawdown of the portfolio equity. In contrast to references Chekhlov, Uryasev, and Zabarankin (2003, 2005), Goldberg and Mahmoud (2017), and Zabarankin, Pavlikov, and Uryasev (2014), who used the absolute drawdown, our risk measure is based on the relative drawdown process. Combined with the results of Part I, Maier-Paape and Zhu (2018), this allows us to calculate efficient portfolios based on a drawdown risk measure constraint. Full article

(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)

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35 pages, 500 KiB

Open AccessArticle

A General Framework for Portfolio Theory—Part I: Theory and Various Models

by Stanislaus Maier-Paape and Qiji Jim Zhu

Risks 2018, 6(2), 53; https://doi.org/10.3390/risks6020053 - 8 May 2018

Cited by 13 | Viewed by 5833

Abstract

Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two-dimensional space of utility and risk. This is a rather [...] Read more.

Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two-dimensional space of utility and risk. This is a rather general pattern. The modern portfolio theory of Markowitz (1959) and the capital market pricing model Sharpe (1964), are special cases of our general framework when the risk measure is taken to be the standard deviation and the utility function is the identity mapping. Using our general framework, we also recover and extend the results in Rockafellar et al. (2006), which were already an extension of the capital market pricing model to allow for the use of more general deviation measures. This generalized capital asset pricing model also applies to e.g., when an approximation of the maximum drawdown is considered as a risk measure. Furthermore, the consideration of a general utility function allows for going beyond the “additive” performance measure to a “multiplicative” one of cumulative returns by using the log utility. As a result, the growth optimal portfolio theory Lintner (1965) and the leverage space portfolio theory Vince (2009) can also be understood and enhanced under our general framework. Thus, this general framework allows a unification of several important existing portfolio theories and goes far beyond. For simplicity of presentation, we phrase all for a finite underlying probability space and a one period market model, but generalizations to more complex structures are straightforward. Full article

(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)

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22 pages, 587 KiB

Open AccessArticle

Modelling and Forecasting Stock Price Movements with Serially Dependent Determinants

by Rasika Yatigammana, Shelton Peiris, Richard Gerlach and David Edmund Allen

Risks 2018, 6(2), 52; https://doi.org/10.3390/risks6020052 - 7 May 2018

Cited by 2 | Viewed by 5848

Abstract

The direction of price movements are analysed under an ordered probit framework, recognising the importance of accounting for discreteness in price changes. By extending the work of Hausman et al. (1972) and Yang and Parwada (2012),This paper focuses on improving the forecast performance [...] Read more.

The direction of price movements are analysed under an ordered probit framework, recognising the importance of accounting for discreteness in price changes. By extending the work of Hausman et al. (1972) and Yang and Parwada (2012),This paper focuses on improving the forecast performance of the model while infusing a more practical perspective by enhancing flexibility. This is achieved by extending the existing framework to generate short term multi period ahead forecasts for better decision making, whilst considering the serial dependence structure. This approach enhances the flexibility and adaptability of the model to future price changes, particularly targeting risk minimisation. Empirical evidence is provided, based on seven stocks listed on the Australian Securities Exchange (ASX). The prediction success varies between 78 and 91 per cent for in-sample and out-of-sample forecasts for both the short term and long term. Full article

(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)

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20 pages, 620 KiB

Open AccessArticle

Credit Risk Analysis Using Machine and Deep Learning Models

by Peter Martey Addo, Dominique Guegan and Bertrand Hassani

Risks 2018, 6(2), 38; https://doi.org/10.3390/risks6020038 - 16 Apr 2018

Cited by 161 | Viewed by 38875

Abstract

Due to the advanced technology associated with Big Data, data availability and computing power, most banks or lending institutions are renewing their business models. Credit risk predictions, monitoring, model reliability and effective loan processing are key to decision-making and transparency. In this work, [...] Read more.

Due to the advanced technology associated with Big Data, data availability and computing power, most banks or lending institutions are renewing their business models. Credit risk predictions, monitoring, model reliability and effective loan processing are key to decision-making and transparency. In this work, we build binary classifiers based on machine and deep learning models on real data in predicting loan default probability. The top 10 important features from these models are selected and then used in the modeling process to test the stability of binary classifiers by comparing their performance on separate data. We observe that the tree-based models are more stable than the models based on multilayer artificial neural networks. This opens several questions relative to the intensive use of deep learning systems in enterprises. Full article

(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)

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Review

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25 pages, 2834 KiB

Open AccessReview

Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations

by Andreas Mühlbacher and Thomas Guhr

Risks 2018, 6(2), 42; https://doi.org/10.3390/risks6020042 - 23 Apr 2018

Cited by 2 | Viewed by 4987

Abstract

We review recent progress in modeling credit risk for correlated assets. We employ a new interpretation of the Wishart model for random correlation matrices to model non-stationary effects. We then use the Merton model in which default events and losses are derived from [...] Read more.

We review recent progress in modeling credit risk for correlated assets. We employ a new interpretation of the Wishart model for random correlation matrices to model non-stationary effects. We then use the Merton model in which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used, the correlations of which have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary, which also influences the tails. We account for the asset fluctuations by averaging over an ensemble of random matrices that models the truly existing set of measured correlation matrices. As a most welcome side effect, this approach drastically reduces the parameter dependence of the loss distribution, allowing us to obtain very explicit results, which show quantitatively that the heavy tails prevail over diversification benefits even for small correlations. We calibrate our random matrix model with market data and show how it is capable of grasping different market situations. Furthermore, we present numerical simulations for concurrent portfolio risks, i.e., for the joint probability densities of losses for two portfolios. For the convenience of the reader, we give an introduction to the Wishart random matrix model. Full article

(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)

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