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This presentation is based on a part of an academic course on Advanced Enterprise Risk Management (Advanced ERM) titled ‘Risk measures and Measuring, managing and mitigating market, credit and operational risk’ and covers topics such as: mathematical underpins, market risk, credit risk, operational risk and managing market, credit and operational risk. It also includes appendices covering: VaR coherence and VaR vs TVaR, GARCH models, Maximum Likelihood Estimation (MLE), principal components analysis (PCA) and hazard rates and fitting operational risk loss distributions

Slides

1	Session 2: Risk measures and Measuring, managing and mitigating market, credit and operational risk
2	Session 2: Risk measures and Measuring, managing and mitigating market, credit and operational risk
3	Model evolution characteristics
4	Whatever we do requires
5	Terminology
6	Defining value and applicable axioms
7	What if no suitable market in asset or liability?
8	Worth noting implication on loss definition
9	Assumed future behaviour of assets and liabilities
10	More generally
11	Most this course can realistically do
12	Case study / scenario
13	Selection of risk measures
14	Advantages and disadvantages of VaR
15	TVaR has certain technical advantages over VaR
16	Mathematical definitions of VaR and TVaR
17	VaR estimation
18	VaR closely linked to capital requirements
19	VaR and expected/unexpected loss
20	Other risk measures, e.g.
21	Marginal risk, e.g. marginal VaR (MVaR)
22	The Gaussian case
23	Incremental risk, e.g. incremental VaR (IVaR)
24	Risk budgeting
25	Statistical techniques for estimating risk measures
26	Parametric approach
27	Issues
28	Incomplete or out-of-date data
29	Non-linear exposures
30	Call option price
31	Heteroscedasticity
32	Non-parametric approach: order statistics
33	Standard errors in non-parametric approach
34	Empirical studies of VaR estimates
35	Back testing
36	Basel back testing rules for banks
37	Session 2: Risk measures and Measuring, managing and mitigating market, credit and operational risk
38	Market risk
39	Typical approaches (1)
40	Typical approaches (2)
41	New directions for market risk: IRC
42	New directions for market risk: Stress VaR
43	Session 2: Risk measures and Measuring, managing and mitigating market, credit and operational risk
44	Credit risk
45	Market developments
46	Implications of new credit markets
47	Credit portfolio risk models
48	Ratings-based models
49	Ratings-based models: components
50	Latent variables
51	Example
52	Pros and cons of ratings based models
53	Equity-based credit portfolio risk models
54	Equity and debt as options on asset value
55	Implementing an equity-based credit risk model
56	Implementing the model statistically
57	Default trigger
58	Strengths and weaknesses of equity-based models
59	Mixture models (1)
60	Mixture models (2)
61	Implementation issues for either type of model
62	Broader issues
63	Session 2: Risk measures and Measuring, managing and mitigating market, credit and operational risk
64	Operational Risk
65	Agency problems, monitoring and control
66	More controls or more control?
67	An illustrative game theoretic model of fraud
68	Equilibria
69	Characteristics of intermittent fraud equilibrium
70	Managing operational risk in practice
71	Benchmarking processes and losses versus others
72	Sharing data
73	Capital for Operational Risk
74	Insurance as a substitute for capital
75	Session 2: Risk measures and Measuring, managing and mitigating market, credit and operational risk
76	Managing market, credit and operational risk
77	Any action to reduce one risk can increase another
78	Quantifying risk transformation risks
79	Main 'market' hedging instruments
80	Dynamic hedging (1)
81	Dynamic hedging (2)
82	Risk/reward analysis and asset/exposure allocation
83	Session 2: Agenda covered
84	Session 2: Risk measures and Measuring, managing and mitigating market, credit and operational risk
85	Appendix A: VaR coherence and VaR vs TVaR
86	Axiomatic approach: coherence
87	Characterisation of coherent risk measures
88	VaR is coherent for Gaussian distributions
89	Arguments favouring TVaR based on coherence
90	More generic arguments favouring TVaR
91	Which takes into account loss in the event of default?
92	Different stakeholder perspectives (1)
93	Different stakeholder perspectives (2)
94	Treatment of illiquidity (1)
95	Treatment of illiquidity (2)
96	Treatment of illiquidity (3)
97	Stress testing methodologies
98	Appendix B: GARCH models
99	Properties of GARCH models
100	RiskMetrics approach
101	RiskMetrics specification
102	Appendix C: Maximum Likelihood Estimation
103	Log likelihood
104	Desirable properties of ML estimator
105	Likelihood ratio tests
106	Binomial back testing
107	Introducing a restriction
108	Appendix D: Principal components analysis
109	Principal components - explanation or noise?
110	Smaller eigenvalues/principal components
111	Appendix E: Hazard rates and fitting loss distributions
112	Hazard rates
113	Simple example of a hazard rate
114	Hazard rates that vary through time
115	Simulating independent failure times
116	Incorporating dependence in failure times
117	Fitting loss distributions
118	E.g. Gamma distribution
119	Important Information

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