Delta-normal 3

# Delta-normal 3 - Undergraduate Research Opportunity...

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I Undergraduate Research Opportunity Programme in Science Value at Risk Dai Bo Supervisor: Dr. Arie Harel Department of Mathematics National University of Singapore Academic year (2000/2001)

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II Summary Value at Risk (VaR) is one of the most popular tools used to estimate exposure to market risks, and it measures the worst expected loss at a given confidence level. In this report, we explain the concept of VaR, and then describe in detail some methods of VaR computation. We then discuss some VaR tools that are particularly useful for risk management, including marginal VaR, incremental VaR and component VaR. The next consideration is the effect of time varying risk, which can be estimated by a moving average model or a GARCH process. Finally, we introduce some back testing methods to validate the use of VaR model. All description, definitions, examples, results, proofs, tables, and remarks in this report are taken from the 2nd edition of the book of Philppe Jorion &Value at Risk± (Jorion 2001), unless otherwise indicated.
III Table of contents Cover page I Summary II Table of contents III Chapter 1 Motivation and Introduction 1 1.1 Motivation 1 1.2 Introduction 1 1.3 Overview of the report 2 Chapter 2 VaR computation 3 2.1 Definition of VaR 3 2.2 Measuring returns 3 2.3 Computation of VaR 4 2.4 VaR measurement over different parameters 9 2.5 Choice of parameters 10 Chapter 3 Portfolio VaR 12 3.1 Portfolio VaR for multiple assets 12 3.2 VaR reduction methods 14 3.3 VaR tools 15 Chapter 4 Modeling Time-varying Risk 20 4.1 The existence of time-varying risk 20 4.2 Moving average 21 4.3 GARCH estimation 23 4.4 RiskMetrics approach 27 Chapter 5 Back Testing VaR Models 29 5.1 Model back testing with exceptions 29 5.2 Model back testing with conditional coverage 32 Chapter 6 Conclusions 36 References 37

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1 Chapter 1 Motivation and Introduction 1.1 Motivation One may still remember the name Nicholas Leeson. He was an investment officer of Barings Bank London England and worked in the bank's Singapore office. Mr. Leeson lost 1.3 billion dollars because of risky derivative investments in the Japanese future market. This huge loss wiped out the firm’s entire equity capital and resulted in the financial collapse of one of the world’s largest banks. This financial disaster revealed the absence of enforced risk management policies. In the later studies, it has been shown that under normal market conditions, the potential loss of Mr. Leeson’s trading would exceed 835 million dollars 5 percent of the time. If these calculations had been in place, the parent company could provide some protection against rogue traders and other operational risks, and thus the bank disaster might be avoided. Because Barings was viewed as a conservative bank, the bankruptcy served as a wakeup call for financial institutions all over the world. Thereafter, risk management has emerged and many methodologies were developed for the purpose of risk management.
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## Delta-normal 3 - Undergraduate Research Opportunity...

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