Computational Methods for Risk Management in Economics and Finance Computational Methods for • Marina Resta Risk Management in Economics and Finance Edited by Marina Resta Printed Edition of the Special Issue Published in Risks www.mdpi.com/journal/risks Computational Methods for Risk Management in Economics and Finance Computational Methods for Risk Management in Economics and Finance Special Issue Editor Marina Resta MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin Special Issue Editor Marina Resta University of Genova Italy Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Risks (ISSN 2227-9091) (available at: https://www.mdpi.com/journal/risks/special issues/ Computational Methods for Risk Management). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03928-498-6 (Pbk) ISBN 978-3-03928-499-3 (PDF) c 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editor ...................................... vii Preface to ”Computational Methods for Risk Management in Economics and Finance” .... ix Peter Martey Addo, Dominique Guegan and Bertrand Hassani Credit Risk Analysis Using Machine and Deep Learning Models † Reprinted from: Risks 2018, 6, 38, doi:10.3390/risks6020038 ...................... 1 Andreas M ¨uhlbacherand Thomas Guhr Credit Risk Meets Random Matrices: Coping withNon-Stationary Asset Correlations Reprinted from: Risks 2018, 6, 42, doi:10.3390/risks6020042 ...................... 21 Douw Gerbrand Breed, Tanja Verster, Willem D. Schutte and Naeem Siddiqi Developing an Impairment Loss Given Default Model Using Weighted Logistic Regression Illustrated on a Secured Retail Bank Portfolio Reprinted from: Risks 2019, 7, 123, doi:10.3390/risks7040123 ..................... 47 Stanislaus Maier-Paape and Qiji Jim Zhu A General Framework for Portfolio Theory—Part I: Theory and Various Models Reprinted from: Risks 2018, 6, 53, doi:10.3390/risks6020053 ...................... 63 Stanislaus Maier-Paape and Qiji Jim Zhu A General Framework for Portfolio Theory. Part II: Drawdown Risk Measures Reprinted from: Risks 2018, 6, 76, doi:10.3390/risks6030076 ...................... 99 Marco Neffelli Target Matrix Estimators in Risk-Based Portfolios Reprinted from: Risks 2018, 6, 125, doi:10.3390/risks6040125 .....................131 Takaaki Koike and Marius Hofert Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations Reprinted from: Risks 2020, 8, 6, doi:10.3390/risks8010006 .......................151 Wided Khiari and Salim Ben Sassi On Identifying the Systemically Important Tunisian Banks: An Empirical Approach Based on the CoVaR Measures Reprinted from: Risks 2019, 7, 122, doi:10.3390/risks7040122 .....................185 Rasika Yatigammana, Shelton Peiris, Richard Gerlach and David Edmund Allen Modelling and Forecasting Stock Price Movements with Serially Dependent Determinants Reprinted from: Risks 2018, 6, 52, doi:10.3390/risks6020052 ......................201 v About the Special Issue Editor Marina Resta, Ph.D. is an Assistant Professor at the Department of Economics and Statistics of the University of Genova, Italy. Since 1996, she has worked in the area of financial risk, leading research and commercial projects on: machine learning, forecasting in financial markets, option pricing, actuarial mathematics, and the development of relevant numerical methods and software. She graduated in Economics at the University of Genova, Italy and received a PhD in Applied Economics and Quantitative Methods from the same university. Dr. Marina Resta’s publication records include two monographs and over 130 works, including journal papers, articles in contributed books, and in conference proceedings. vii Preface to ”Computational Methods for Risk Management in Economics and Finance” The aim of the Special Issue is to highlight the relevance of computational methods in economic and financial modeling as an alternative to conventional analytical and numerical paradigms, bringing together both theoretical and application-oriented contributions. We received a large number of submissions, and ultimately published the nine high quality contributions that compose this Issue. The papers address a variety of important issues, mainly focusing on credit risk and risk measures. The research stream of credit risk is debated in three papers. The paper of Peter Martey Addo, Dominique Guegan, Bertrand Hassani (Addot et al., 2018) addresses questions related to the intensive use of deep learning systems in enterprises to predict loan default probability. Andreas Muhlbacher¨ and Thomas Guhr (Muhlbacher¨ and Guhr, 2018) examine the issue of modeling credit risk for correlated assets. Employing a new interpretation of the Wishart model for random correlation matrices, they model non-stationary effects and show how their approach can grasp different market situations. Douw Gerbrand Breed, Tanja Verster, Willem D. Schutte, and Naeem Siddiqi (Breed et al., 2019) propose a method based on weighted logistic regression to model loss given default for IFRS 9 purposes. The Special Issue also has a number of contributions dealing with portfolio theory and risk measures. The first contribution of Stanislaus Maier-Paape and Qiji Jim Zhu (Maier-Paape and Zhu, 2018a) debates the mathematical representation of the trade-off between utility and risk, thus introducing a general framework for portfolio theory that allows a unification of several important existing portfolio theories. The second contribution (Maier-Paape and Zhu, 2018b) provides several examples of convex risk measures necessary for the application of the above-discussed general framework, with a special focus on risk measures related to the “current” drawdown of the portfolio equity. The focus is maintained on risk-based portfolios in the paper of Marco Neffelli (Neffelli, 2018), who compares various estimators for the sample covariance matrix. Using extensive Monte Carlo simulations, the author offers a comparative study of these estimators, testing their ability to reproduce the true portfolio weights. Takaaki Koike and Marius Hofert (Koike and Hofert, 2020) use Markov chain Monte Carlo (MCMC) methods to estimate systemic risk measures and risk allocations. The efficiency of the MCMC estimators is demonstrated in a series of numerical experiments. The remaining contributions address practical issues: Wided Khiari and Salim Ben Sassi (Khiari and Ben Sassi, 2019) assess the systemic risk of Tunisian listed banks by way of CoVaR; finally, Rasika Yatigammana, Shelton Peiris, Richard Gerlach, and David Edmund Allen (Yatigammana et al, 2018) analyze the direction of price movements under an ordered probit framework, and provide empirical evidence based on stocks listed on the Australian Securities Exchange (ASX). ix All papers appearing in this Special Issue went through a refereeing process subject to the usual high standards of Risks. I would like to thank all the authors for their contribution and all the referees for their thorough and timely reviews. I would also like to express my gratitude to the editor of Risks, to the Assistant Editors, and to MDPI for their support in the editorial process. I hope that this Special Issue will help to stimulate the debate on using computational methods in economic and financial modeling from both theoretical and applied perspectives. Marina Resta Special Issue Editor x risks Article Credit Risk Analysis Using Machine and Deep † Learning Models Peter Martey Addo 1,2,*, Dominique Guegan 2,3,4 and Bertrand Hassani 2,4,5,6 1 Direction du Numérique, AFD—Agence Française de Développement, Paris 75012, France 2 Laboratory of Excellence for Financial Regulation (LabEx ReFi), Paris 75011, France; [email protected] (D.G.); [email protected] (B.H.) 3 IPAG Business School, University Paris 1 Pantheon Sorbonne, Ca’Foscari Unversity of Venezia, Venezia 30123, Italy 4 Université Paris 1 Panthéon-Sorbonne, CES, 106 bd de l’Hôpital, Paris 75013, France 5 Capgemini Consulting, Courbevoie 92400, France 6 University College London Computer Science, 66-72 Gower Street, London WC1E 6EA, UK * Correspondence: [email protected]; Tel.: +33-638-308-228 † The opinions, ideas and approaches expressed or presented are those of the authors and do not necessarily reflect any past or future Capgemini’s positions. As a result, Capgemini cannot be held responsible for them. Received: 9 February 2018; Accepted: 9 April 2018; Published: 16 April 2018 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, we build binary classifiers based on machine and