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RMBI 4210 – Quantitative Methods for Risk Management
Spring semester, 2018
Course Home Page
http://www.math.ust.hk/~maykwok/RMBI 4210.htm
Please check the course home page regularly for updated information regarding the course.
Instructor
Professor Yue Kuen KWOK
Contact Details: Office in Room 3445; phone: 2358-7418; e-mail: [email protected]
Office Hour: Monday, 2:30pm - 3:30pm
Meeting Time and Venue
Lectures
Monday, 15:00pm – 16:20pm and Friday, 10:30am-11:50am, Room 6591
Tutorials (conducted by Dr Jingjing Wang, [email protected])
Wednesday, 18:00pm-18:50pm, Room 1103
Course Objective and Description
This course illustrates the use of various quantitative methods: statistical analysis, simulation and
optimization methods, in the modeling and management of financial risks. The topics include
characterization of financial risks, hedging of market risk, basis risk, liquidity risk, credit portfolio
and loss distribution, Value-at-Risk and expected shortfall, coherent measures of risk and
economic capital, credit yield curves, credit derivatives: credit default swaps and collateralized
debt obligations, Bernoulli mixture models, default correlation, copula functions, CreditMetrics,
factor models.
Course Content
1. Financial risks: loss distributions and risk measures
1.1 Types of financial risks
Black Monday in 1987: Market failure arising from program trading
Systemic risk: Wall Street fails Main Street
Market risk: Dynamic hedging of options
Basis risk
Credit risk: Loan portfolio losses
Liquidity risk: Bid-ask spread
Operational / Model / Legal risks
Fitting of loss distribution
1.2 Credit rating
Balance sheet scorings: S&P and Moody ratings
Structural approach: KMV model
1.3 VaR (Value-at-Risk), expected shortfall: coherent risk measures
VaR calculations
Expected shortfall
Coherent risk measures
Risk control for expected utility-maximizing investors
Economic capital
Risk-adjusted return
Extreme value theory
2. Bond risks and credit derivatives
2.1 Implied probability of default
Credit yield curves
Credit spread and default intensities
2.2 Credit default swaps
Funding cost arbitrage
Counterparty risk
Fair valuation of protection premium
Uses in synthetic Collateralized Debt Obligations
2.3 Credit spread and bond price based pricing of credit derivatives
Implied hazard rate
Building blocks of credit derivatives pricing
3. Default correlation modeling
3.1 Mixture models for modeling default correlation
Bernoulli mixture models
Moody’s binomial expansion method
Contagion models
3.2 CreditMetrics and copula functions
Credit migration
CreditMetrics
Copula functions
Exponential models for defaults
3.3 Global correlation model using factor models approach
Factor models
Principal component analysis
Monte Carlo simulation method
3.4 Correlation products: pricing of Collateralized Debt Obligations
Product features of Collateralized Debt Obligations
One-factor Gaussian copula model
Assessment Scheme
The assessment is based on the mid-term test, final examination and reading assignments.
Grading policies
80-minute mid-term test 30%
160-minute final examination 60%
One reading assignment (AIG bailout) 10%
Due on April 16 (Monday)
Date of the mid-term test
26 March (Monday) during the lecture hour
Student Learning Resources
Lecture Notes:
Lecture notes and homework set can be downloaded from the course home page.
References
1. Hull, J., Risk Management and financial institution, 4th edition (2015), Prentice Hall.
(downloadable from HKUST Library)
2. Jorion, P., Financial risk manager handbook plus test bank: FRM Part I/Part II (2011),
John Wiley & Sons.
3. Bluhm, C., Overbeck, L., Wagner, C., Introduction to credit risk modeling, second
edition (2010), Chapman & Hall/CRC.
Teaching Approach
Lectures:
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 models
Review of industrial practices in risk management and lessons learned from real life
credit cases.
Tutorials: worked examples and problem solving skills.
Intended Learning Outcomes
Upon successful completion of this course, students should be able to understand:
1. Nature of various forms of financial risks: market risk, credit risk, basis risk and liquidity
risk
2. Quantitative measures of portfolio risk using VaR and expected shortfall, and their
limitations.
3. Set economic capital and determine risk-adjusted return on capital?
4. Estimation of VaR and expected shortfall using extreme value theory
5. Generate the credit yield curves from tradeable prices of defaultable bonds
6. Understand funding cost arbitrage and counterparty risk of credit default swaps
7. Derive the implied hazard rate from zero-coupon bond prices and build the building blocks
for pricing credit derivatives,
8. Model default correlation among risky obligors using the mixture models?
9. Understand the popular industrial code CreditMetrics for modeling credit portfolio risk.
10. Understand the role of copula functions to model default correlation.
11. Factor models and principal component analysis.
12. Generate the loss distribution of a portfolio of risky assets using Monte carlo simulation
13. Product nature of the Collateralized Debt Obligations and pricing using the Gaussian
copula model
Course Schedule
Week Content Remarks
1 Systemic risk, hedging market risk Topic 1.1
2 Basis risk and credit risk; portfolio losses and credit ratings Topic 1.2
3 Coherent risk measures: VaR and expected shortfall Topic 1.3
4 Economic capital and extreme value theory Topic 1.4
5 Implied probability of default and credit yield curves Topic 2.1
6 Credit default swaps Topic 2.2
7 Pricing of credit derivatives Topic 2.3
8 Mixture models for modeling default correlation Topic 3.1
9 CreditMetrics and copula Topic 3.2
10 Factor models and principal component analysis Topic 3.3
11 Collateralized debts obligations Topic 3.4
