Complete Summary New Developments in Risk Management

Summary NDRM
New 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