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Topics in Financial Market Risk Modelling TOPICS IN FINANCIAL MARKET RISK MODELLING Zishun Ma A DISSERTATION in Quantitative Finance In partial fulfillment of the Requirements for the Degree of Doctor of Philosophy 25/10/2012 Newcastle Business School Newcastle University Newcastle Upon Tyne, UK 1 To my Grandmother 2 Acknowledgement Studying for a PhD has been a valuable and indispensable experience in my life. When looking back, I am delighted and at same time grateful for all I have received throughout these three years. I would like to express my deep and sincere gratitude to my two supervisors, Prof. Robert Sollis and Dr. Hugh Metcalf, for their generous encouragement and thoughtful guidance. Prof. Sollis’s and Dr. Metcalf’s wide knowledge and helpful advice provided a solid basis for this present thesis. Dr. Metcalf’s understanding, encouragement and personal guidance have been invaluable to me on both an academic and a personal level. Without their support, this thesis would not have been possible. I am also deeply indebted to my colleagues and friends in the Newcastle Business School that have provided the environment for sharing their experiences and thoughts with me. I would especially like to thank my two colleagues and best friends, Hangxiong Zhang and Fengyuan Shi, for their extremely valuable support and insights in my PhD study. I own my loving thanks to my parents, Lilin Wang and Chenggang Ma, and my beloved girlfriend, Yongying Yu. Their selfless love and care have provided me inspiration and power. Without their encouragement and understanding it would have been impossible for me to finish this work. I owe them everything and here I just wish to show them how much I love and appreciate them. Finally I would like to thank all of people and friends whom I know for their help. 3 DECLARATION OF AUTHENTICITY This thesis contains no material which has been accepted for the award of any other degree or diploma in any University, and is less than 100,000 words in length. To the best of my knowledge and belief, this thesis contains no material previously published or written by another person, except where due reference has been made. 4 Abstract The growth of the financial risk management industry has been motivated by the increased volatility of financial markets combined with the rapid innovation of derivatives. Since the 1970s, several financial crises have occurred globally with devastating consequences for financial and non-financial institutions and for the real economy. The most recent US subprime crisis led to enormous losses for financial and non-financial institutions and to a recession in many countries including the US and UK. A common lesson from these crises is that advanced financial risk management systems are required. Financial risk management is a continuous process of identifying, modeling, forecasting and monitoring risk exposures arising from financial investments. The Value at Risk (VaR) methodology has served as one of the most important tools used in this process. This quantitative tool, which was first invented by JPMorgan in its Risk-Metrics system in 1995, has undergone a considerable revolution and development during the last 15 years. It has now become one of the most prominent tools employed by financial institutions, regulators, asset managers and nonfinancial corporations for risk measurement. My PhD research undertakes a comprehensive and practical study of market risk modeling in modern finance using the VaR methodology. Two newly developed risk models are proposed in this research, which are derived by integrating volatility modeling and the quantile regression technique. Compared to the existing risk models, these two new models place more emphasis on dynamic risk adjustment. The empirical results on both real and simulated data shows that under certain circumstances, the risk prediction generated from these models is more accurate and efficient in capturing time varying risk evolution than traditional risk measures. Academically, the aim of this research is to make some improvements and extensions of the existing market risk modeling techniques. In practice, the purpose of this research is to support risk managers developing a dynamic market risk measurement system, which will function well for different market states and asset categories. The system can be used by financial institutions and non-financial institutions for either passive risk measurement or active risk control. Key words: Value at Risk, Volatility modeling, Risk mapping, Monte Carlo Simulation, Quantile regression 5 Table of Contents Table of figures .......................................................................................................................... 9 1 Introduction ........................................................................................................................... 11 1.1 The need for the financial risk management .................................................................. 11 1.2 General introduction of Value at Risk in the financial risk management ...................... 13 1.3 Research contributions of the thesis ............................................................................... 14 1.4 Structure of the thesis ..................................................................................................... 18 2 Literature review of the financial market risk modeling ...................................................... 20 2.1 Building blocks of Value at Risk models ....................................................................... 20 2.1.1 Non-parametric VaR model ..................................................................................... 21 2.1.2 Parametric VaR model ............................................................................................. 22 2.1.3 Semi-parametric VaR model and Extreme Value Theory ....................................... 24 2.1.4 CAViaR model ......................................................................................................... 26 2.2 Combining risk exposure modeling with VaR models ................................................... 28 2.2.1 Local-valuation approach ......................................................................................... 29 2.2.2 Full-valuation approach............................................................................................ 31 2.3 Risk decomposing by VaR models ................................................................................. 34 2.3.1 Marginal VaR ........................................................................................................... 34 2.3.2 Incremental VaR and best hedge ratio ..................................................................... 35 2.4 Risk integration techniques ............................................................................................ 36 2.4.1 Regression analysis .................................................................................................. 37 2.4.2 Principle Component Analysis ................................................................................. 38 2.5 Risk overlay on multi-time horizon ................................................................................ 39 2.5.1 Factors considered in the VaR models ..................................................................... 40 2.5.2 Multi-day VaR from IGARCH model ..................................................................... 40 2.5.3 Multi-day VaR from ARMA-GARCH model ......................................................... 42 2.5.4 An ideal of accuracy improvement .......................................................................... 44 2.6 Conclusion ...................................................................................................................... 45 3 Application of VaR models in the financial market risk measurement ................................ 47 3.1 Dataset ............................................................................................................................ 47 3.2 Risk measurement of the equity portfolio ...................................................................... 48 3.2.1 Equity risk assessment ............................................................................................. 49 3.2.2 Risk integration of the equity portfolio .................................................................... 51 3.2.3 Time varying conditional distribution on VaR estimates ........................................ 54 6 3.3 Risk measurement of the future and option portfolio ..................................................... 58 3.3.1 Empirical results from Local valuation approach .................................................... 59 3.3.2 Empirical results from Full valuation approach ....................................................... 63 3.4 Risk measurement of the foreign currency ..................................................................... 66 3.4.1 Findings from the local valuation approach ............................................................. 66 3.4.2 Empirical analysis .................................................................................................... 68 3.5 Risk measurement of the bond portfolio ........................................................................ 72 3.5.1 Risk profile analysis in the UK bond market ........................................................... 72 3.5.2 Risk measurement integrating the mapping techniques ..........................................
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