ESSAYS ON RISK MANAGEMENT

Abstract

Risk management is the process by which various financial risk exposures are identified, measured, and controlled. Financial risks can be defined as those that relate to possible losses in financial markets, such as losses due to interest rate movements or defaults on financial obligations. Generally, financial risks are classified into the broad categories of market risks, credit risks, liquidity risks, operational risks, and legal risks. This dissertation comprises three essays on risk management. In the first essay “Stress Testing for Two-stage Transmission Stress Events”, we use the two-stage conditional probability distributions to compute a new loss exposure measure for stress events that may have two-stage sequential impacts on various markets. The simulated results show that the proposed loss exposure measure improves upon the over- or under-estimation biases commonly found in stress testing conducted by financial institutions in their VaR calculations. In the second essay “Estimating Extreme Correlation for the EVT-type VaR - a Copula Approach”, we propose to use the Clayton copula to derive a time-varying correlation model for calculating the extreme value theory (EVT) type Value at Risk (VaR). Using a historical VaR as benchmark, the results show that on average, the new approach outperforms that with constant correlation, especially in portfolios with less risk exposure to the NTD/USD foreign exchange rate. In the third essay “A Poisson Model with Common Shocks for CDO Valuation”, we propose a collateralized debt obligation (CDO) valuation model without having to assume conditional independence. A Poisson model with common shocks is used for the derivation of CDO loss function. By grouping firms with equal credit ratings, the number of model parameters is reduced. Thereby, the implementation of models assuming conditional dependence can be made more efficient.Table of Contents Introduction 1 ESSAY 1: Stress Testing for Two-stage Transmission Stress Events 3 Chapter I. Introduction……………………………………………………… 5 Chapter II. A Hypothesis on Two-stage Transmission………………………. 7 Chapter III. Stress Testing for Two-stage Transmission……………………… 9 Chapter IV. Historical Simulation Test………………………………………. 12 Chapter V. Concluding Remarks……………………………………………. 18 Appendix………………………………………………………………………… 19 References……………………………………………………………………….. 25 ESSAY 2: Estimating Extreme Correlation for the EVT-type VAR—A Copula Approach 26 Chapter I. Introduction……………………………………………………… 28 Chapter II. Computation of the EVT-type VaR……………………………… 31 Chapter III. An Empirical Comparison………………………………………. 36 Chapter IV. Conclusion………………………………………………………. 47 Appendix………………………………………………………………………… 48 References……………………………………………………………………….. 52 ESSAY 3: A Poisson Model with Common Shocks for CDO Valuation 54 Chapter I. Overviews of CDOs………………………………………………56 Chapter II. Review of CDO's Valuation Approaches…………………………58 Chapter III. The CDO Proposed Valuation Methodology……………………. 61 Chapter IV. Numerical Illustrations………………………………………….. 67 Chapter V. Conclusion………………………………………………………. 72 Appendix …………………………………………………………………………73 References……………………………………………………………………….. 7