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Complete Summary New Developments in Risk Management
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Complete summary: Lectures, tutorials & Articles of New developments in Risk Management (NDRM).
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Summary NDRMNew Developments in Risk Management
2023/2024
Week 1.......................................................................................................................................................... 3
Tutorial.................................................................................................................................................................5
,Week 2.......................................................................................................................................................... 6
Lecture..................................................................................................................................................................6
Week 3........................................................................................................................................................ 10
Lecture................................................................................................................................................................10
Tutorial...............................................................................................................................................................13
Week 4........................................................................................................................................................ 15
Lecture........................................................................................................................................................ 15
Tutorial...............................................................................................................................................................17
Week 5........................................................................................................................................................ 20
Lecture................................................................................................................................................................20
Tutorial...............................................................................................................................................................23
Week 6........................................................................................................................................................ 28
Lecture................................................................................................................................................................28
Tutorial...............................................................................................................................................................30
Articles........................................................................................................................................................ 34
Week 1................................................................................................................................................................34
Article 1: Value at risk and Extreme returns..................................................................................................34
Week 2................................................................................................................................................................34
Article 1: Compliance governance.................................................................................................................34
Article 3: Supervisory landscape....................................................................................................................35
Article 4: Legal embedding of compliance function......................................................................................37
Article 5: Integrity and integrity risks............................................................................................................37
Week 3................................................................................................................................................................38
Article 1: On the value of Virtual currencies..................................................................................................38
Week 4................................................................................................................................................................41
Article 1: IMF Operational resilience in digital payments..............................................................................41
Week 5................................................................................................................................................................41
Article 1: SRB Expectations for banks............................................................................................................41
Article 2: SRB Introduction to resolution planning........................................................................................42
Article 3: SRB Resolution Q&A.......................................................................................................................42
Week 6................................................................................................................................................................42
Article 1: IAIS The impact of climate change on the financial stability of the insurance sector...................42
Article 2: Application paper on the supervision of climate-related risks in the insurance sector................43
Article 3: DNB managing climate and environmental risks...........................................................................43
, Week 1
Lecture
Financial risk uncertainty/randomness uncertainty means a single
value prediction is always wrong
Risk probabilities
Tail risk small probabilities (sometimes probability of events we have
never seen before)
Calculate Value-at-Risk methods
1. Normal distribution
2. Historical distribution
3. Power law tail (heavy tails)
Method 1: Normal distribution
μ+ z∗σ
, μ=average daily return ≈ 0
z=z-score , depends on probability
σ =standard deviation ( estimate¿ data:0.95 % )
Problem: tail of normal distribution is too thin exponential-type
shape
Method 2: Historical distribution
Rank n historical returns from low to high
Take n*(100%-x%)th worst observation
Don’t rely on assuming a specific distribution
Accurate when historical sample of returns reflects future risk
High estimation uncertainty when looking at smaller probabilities
Method 3: Power law tail
Pr(loss > u) = Cu-
C = scale parameter
= tail index (usually 2 5)
Results in more probability mass for extreme outcomes than the
normal distribution heavy/fat tails
For financial assets, if you collect a lot of return data something
interesting happens
Verify if log10 p = a – b log10 u implies p = Cu-
C 1/ α
VaR = ( ¿ ¿ p = 0.01 for VaR at confidence level 99%
p
Hill estimator
Estimate from the k largest losses in the data
750 n 2500, set k at ≈ 5 % of n
Sort losses (positive numbers) from large to small largest is X1,
second largest is X2 etc.
Does not always fit the tail of return distribution well
Remarks
Models are estimated based on limited amount of random data
number you calculate is never precisely VaR the further in the tail,
the larger the estimation uncertainty
Backward-looking risk models do historical returns reflect future
risk?
How much historical data to use?
Did the risk characteristics of the underlying asset change?
Yes? choose shorter estimation horizon
Are you interested in extremely small probability events?
Yes? choose longer estimation horizon
Depending on purpose typical applications with daily
data use 2-10 years of returns
Volatility clustering periods of high and low volatility can result
in several VaR exceptions in a short period of time
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