Georgia State University ScholarWorks @ Georgia State University Risk Management and Insurance Dissertations Department of Risk Management and Insurance 8-1-2014 Essays on Financial Risk Modeling and Forecasting Jinyu Yu Follow this and additional works at: https://scholarworks.gsu.edu/rmi_diss Recommended Citation Yu, Jinyu, "Essays on Financial Risk Modeling and Forecasting." Dissertation, Georgia State University, 2014. https://scholarworks.gsu.edu/rmi_diss/35 This Dissertation is brought to you for free and open access by the Department of Risk Management and Insurance at ScholarWorks @ Georgia State University. It has been accepted for inclusion in Risk Management and Insurance Dissertations by an authorized administrator of ScholarWorks @ Georgia State University. For more information, please contact [email protected]. PERMISSION TO BORROW In presenting this dissertation as a partial fulfillment of the requirements for an advanced degree from Georgia State University, I agree that the Library of the University shall make it available for inspection and circulation in accordance with its regulations governing materials of this type. I agree that permission to quote from, to copy from, or publish this dissertation may be granted by the author or, in his/her absence, the professor under whose direction it was written or, in his ab- sence, by the Dean of the Robinson College of Business. Such quoting, copying, or publishing must be solely for the scholarly purposes and does not involve potential financial gain. It is understood that any copying from or publication of this dissertation which involves potential gain will not be allowed without written permission of the author. Jinyu Yu NOTICE TO BORROWERS All dissertations deposited in the Georgia State University Library must be used only in accordance with the stipulations prescribed by the author in the preceding statement. The author of this dissertation is: JINYU YU DEPARTMENT OF RISK MANAGEMENT AND INSURANCE 35 BROAD ST. NW, ATLANTA, GA 30303 The director of this dissertation is: RICHARD LUGER DEPARTMENT OF RISK MANAGEMENT AND INSURANCE 35 BROAD ST. NW, ATLANTA, GA 30303 Essays on Financial Risk Modeling and Forecasting BY JINYU YU A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree Of Doctor of Philosophy In the Robinson College of Business Of Georgia State University GEORGIA STATE UNIVERSITY ROBINSON COLLEGE OF BUSINESS 2014 Copyright by JINYU YU 2014 i ACCEPTANCE This dissertation was prepared under the direction of the Jinyu Yu's Dissertation Committee. It has been approved and accepted by all members of that committee, and it has been accepted in partial fulfillment of the requirements for the degree of Doctoral of Philosophy in Business Administration in the J. Mack Robinson College of Business of Georgia State University. H. Fenwick Huss, Dean DISSERTATION COMMITTEE RICHARD LUGER AJAY SUBRAMANIAN DANIEL BAUER PIERRE NGUIMKEU ii ABSTRACT Essays on Financial Risk Modeling and Forecasting BY Jinyu Yu May 30, 2014 Committee Chair: Richard Luger Major Academic Unit: Department of Risk Management and Insurance The first chapter examines statistical inference in the context of a generalized version of the widely used Vasicek credit default model, whereby the purely static model is extended to allow for autocor- related default rates and macroeconomic risk factors. The proposed inference method proceeds by numerically inverting a likelihood ratio test and then it exploits projection techniques to produce simultaneous confidence intervals for general non-linear functions of the model parameters, includ- ing multi-step ahead expected losses. An extensive simulation study reveals that the new method outperforms Delta method and even the usual residual and parametric bootstrap procedures. The results of an empirical application to U.S. bank loan losses show that moving from the static to the dynamic default rate distribution significantly lowers the implied economic capital requirements. The second chapter studies long-term risk management which has gained great importance following several tremendous financial crises. It focuses on the 10-day and 30-day ahead forecast of the most popular tail risk measure, value-at-risk(VaR). Two categories of approaches are utilized: 1, direct iii VaR forecast by square-root-of-time rule (SRTR) and pseudo return generation by GARCH model, using Monte Carlo Simulation (GARCH-MC). 2, indirect VaR forecast through a volatility forecast by autoregressive models of realized volatility and mixed-frequency sampling (MIDAS) method. By an extensive comparison of out-of-sample forecasts and back-testing statistics, it is shown that SRTR combined with Cornish-Fisher approximation outperforms the alternatives and provides adequate forecasting accuracy. The possible reason is that serial correlation is not significant in the returns and the effects of other stylized facts in returns offset each other. The indirect forecast approach does not perform as well as the direct approach. The last chapter proposes an innovative approach of forecasting swap spreads. It is shown that swap spreads and the risk factors tend to be random walk processes, and the residual obtained from regressing swap spread on a set of contemporaneous risk factors is a mean-reverting process. Information contained in the residual is explored by using it as the predictor of future swap spread. In terms of forecasting methodology, this chapter introduces an efficient and simple method through modeling residual as an Ornstein-Uhlenbeck (OU) process. The forecasting is implemented over a continuous set of horizons from 1 day to 200 days. Two measures of forecasting errors are utilized: mean squared error (MSE) and mean absolute error(MAE). By comparing errors of both in-sample and out-of-sample forecasting, evidence is found that the residual obtained from a contemporaneous regression of swap spreads on the risk factors contains significant predicative information. Moreover, modeling residual as an OU process achieves superior forecasting performance than the alternatives. iv ACKNOWLEDGMENTS The completion of this dissertation has required a lot of guidance and assistance from many people, to whom I will forever be grateful. First of all, I would like to express the deepest appreciation to my committee chair, Professor Richard Luger, who has continually conveyed a spirit of adventure in regard of research and great inspiration in regard of teaching. Without his persistent guidance and assistance, this dissertation would not have been possible. I also want to thank my other three committee members: Professor Ajay Subramanian, Professor Daniel Bauer and Professor Pierrer Nguimkeu, who have been nothing but helpful and insightful in the process of advising my dis- sertation. All their comments and suggestions have been extremely useful and highly appreciated. Possible errors and shortcomings in this dissertation are my responsibility. It has been such an honor for me to study in this excellent Ph.D. program, where I have learned and benefited more than I could ever imagine. I owe the sincere gratitude to the department chair, Professor Martin Grace, and the Ph.D. coordinators: Professor Ajay Subramanian, Professor George Zanjani and Professor Stephen Shore. Their insights and suggestions have guided me through kinds of academic and career-wise difficulties. A special thank you is owed to Professor Conrad Ciccotello and Professor Vikas Agarwal, who helped me a lot with my first attempt in research and also have advised me so much till today. I also want to thank all faculty and staff members at the department for their kindness and willingness to help. In addition, I am thankful to Adenike Brewington for assisting me with all the detailed administrative matters. I especially appreciate the financial support provided by the Risk Management Foundation (RMF) and Center for the Economic Analysis of Risk (CEAR) at Georgia State University. In addition, my heartfelt thanks go to my fantastic colleagues: Sampan Nettayanun, Xiaohu Ping, Jinjing Wang, who have been with me since day one. The long journey of pursuing the Ph.D. degree would not have been colorful without my amazing friends: Yiling Deng, Philippe d'Astous, Hongjun Ha, Tanya Karelin, Jia Min Ng, Steve Guo, Daniel Quiggin, and Isariya Suttakulpiboon. Last but not least, I would like to express the gratitude to my wonderful husband, Yibiao Lu, who has always been encouraging and believing in me. I also want to thank my parents and brother for loving and caring about me. v CONTENTS ABSTRACT ....................................................................................iii ACKNOWLEDGMENTS . .v CONTENTS . vii LIST OF TABLES . .ix LIST OF FIGURES . x Chapter 1: Simultaneous Confidence Intervals for Dynamic Default Rates . 1 1.1. Introduction . 1 1.2. Default Rate Model . 4 1.3. Capital Calculation . 7 1.4. Projection-Based Methodology . 9 1.5. Simulation . 12 1.6. Empirical Application . 19 1.7. Stress Test . 21 1.8. Conclusion . 23 1.9. Appendix . 41 Chapter 2: Long Term Value-at-Risk Forecasting and Back-Testing . 45 2.1. Introduction . 45 2.2. Direct Forecasting Approach . 48 2.3. Indirect Forecasting Approach: Volatility Transformation . .54 2.4. VaR Back-Testing . .58 2.5. Empirical Results . 64 2.6. Conclusion . 69 2.7. Appendix . 82 vi Chapter 3: Forecasting Interest Rate Swap Spreads: A Residual-Based Approach . 96 3.1. Introduction . 96 3.2. Risk Factors . 99 3.3. Contemporaneous Regression . 101 3.4. Forecasting Methodologies . 105 3.5. Empirical Results . 110 3.6. Conclusion . .113 REFERENCES . .125 vii LIST OF TABLES Table 1.1 Asymptotic Simulation Test: AR Vasicek Model . 25 Table 1.2 Asymptotic Simulation Test: ARX Vasicek Model . .26 Table 1.3 Simulation Results: AR Vasicek . 27 Table 1.4 Simulation Results: ARX(1) Vasicek, unemployment rate . 28 Table 1.5 Simulation Results: ARX(2), unemployment rate+industry production . 29 Table 1.6 Basel II and Static Vasicek Model: parameter estimates . 30 Table 1.7 Parameter Estimates: AR and ARX Vasicek Models . ..