MATH 106



QF5023A - Risk ManagementSummer, 2019Course Home Page check the course home page regularly for updated information regarding the course.InstructorProfessor Yue Kuen KWOK, Hong Kong University of Science and Technology e-mail: maykwok@ust.hkMeeting Time and VenueLecturesAugust 17 (Saturday): 9:30am – 12:00noon; 2:00pm – 4:00pmAugust 18 (Sunday): 9:30am – 12:00noon; 2:00pm – 4:00pmAugust 31 (Saturday): 9:30am – 12:00noon; 2:00pm – 4:00pmSeptember 1 (Sunday): 9:30am – 12:00noon; 2:00pm – 4:00pmCourse Objective and DescriptionThis course illustrates the use of various quantitative techniques (statistical analysis, optimization and simulation methods) and financial engineering principles (hedging and arbitrage), in the quantification and management of financial risks. The topics include immunization of bond risks, credit yield curve modeling, credit default swaps and structured credit products, characterization of financial risks, hedging of market risks, credit portfolio and loss distribution, Value-at-Risk and expected shortfall, coherent measures of risk and economic capital, Bernoulli mixture models, copula functions, CreditMetrics and copula models of default correlation.Course Content1. Financial risks: loss distributions and risk measures1.1 Types of financial risksBlack Monday in 1987: Market failure arising from program trading2010 Flash Crash Systemic risk: Wall Street fails Main StreetCash flow and liquidity riskOperational / Model / Legal risks 1.2 Hedging of market risksDynamic hedging of options1.3 Portfolio loss distributionCredit risk: Loan portfolio lossesFitting of loss distribution1.4 VaR (Value-at-Risk), expected shortfall: coherent risk measuresVaR calculationsExpected shortfall Coherent risk measuresRisk control for expected utility-maximizing investorsEconomic capitalExtreme value theory2. Default correlation models and credit default swapsMixture models and contagion for modeling default correlationBernoulli mixture modelsContagion modelsCreditRisk+ Mixture Poisson distributionIndependent sector risk factorsGeneral sector analysisCreditMetrics Credit migrationCorrelation between changes in credit qualitiesMonte Carlo simulationCopula models of default correlationCopula approachNormal copulaExponential models for defaults Credit default swaps and their usesDefault intensities and probability of defaultProduct nature of credit default swaps: Counterparty riskValuation of credit default swapsUses of credit default swaps: Collateralized Debts Obligations Assessment Scheme The assessment is based on the homework assignment and test. Grading policies16 homework problems15%One reading report on AIG bailout15%80-minute test70%Student Learning Resources Lecture Notes:Lecture notes and homework set can be downloaded from the course home page. ReferencesHull, J., Risk Management and financial institution, 4th edition (2015), Prentice Hall.(downloadable from HKUST Library)Bluhm, C., Overbeck, L., Wagner, C., Introduction to credit risk modeling, second edition (2010), Chapman & Hall/CRC.Teaching ApproachLectures: Focus on the use of quantitative techniques in the modeling of market and credit risks. Emphasize on the quantitative understanding of risk measures, like Value-at-risk and expected shortfall, and their limitations.Understand the mechanism of default correlation via the mixture modelsReview of industrial practices in risk management and lessons learned from real life credit cases. Intended Learning Outcomes Upon successful completion of this course, students should be able to understand:Nature of various forms of financial risks: market risk, credit risk, basis risk and liquidity risk. Hedging of market risk in financial optionsQuantitative measures of portfolio risk using VaR and expected shortfall, and their limitations.Estimation of VaR and expected shortfall using the extreme value theory.Model default correlation among risky obligors using the mixture models. Understand the popular industrial codes, CreditRisk+ and CreditMetrics, for modeling credit portfolio risk.Understand the role of copula functions to model default correlation.Generate the loss distribution of a portfolio of risky assets using Monte carlo simulation Default intensities and calibration of default probabilities from defaultable bond pricesCredit default swaps: counterparty risksValuation of credit default swapsCollateralized Debt Obligations ................
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