15. Risk modelling

Question 1

How would you quantify enterprise risk using dynamic financial analysis?

Answer 1

• Use cashflow models to produce balance sheet and p+l accounts
• Model risks of whole org and relationships between risks

Question 2

How would you quantify enterprise risk using financial condition reports

Answer 2

• Financial condition report: report of current solvency position and possible future development
• Look at risks exposed ro, project expected level of profits and new business, incl. unusual features

Question 3

How would you quantify market risk

Answer 3

• VaR
• Tail VaR
• Interest rate models
• Scenario tests

Question 4

How would you quantify underwriting risk

Answer 4

• Credit risk models for single entity
• Also assessed non-quantitatively e.g. by banks and credit rating agencies

Question 5

How would you quantify credit risk

Answer 5

• Credit risk models for single entity
• Also assessed non-quantitatively e.g. by banks and credit rating agencies

Question 6

How would you quantify liquidity risk

Answer 6

• A+L models

Question 7

How would you quantify operational risk

Answer 7

• Internal and external loss data
• Scenario analysis
• Simulations

Question 8

How would you quantify environmental risk

Answer 8

• Internal and external loss data
• Scenario analysis
• Simulations

Question 9

How would you quantify demographic risk

Answer 9

Quantitative methods

Question 11

Factors to consider when quantifying risk

Answer 11

Extreme events
Data limitations
Interdependence
Unquantifiable risks

Question 12

Outline what correlation is

Answer 12

• Measures how diff variables relate or associate to each other
• Low level: diversify each other to some extent
• Negative: hedge each other

Question 13

Name a linear correlation measure

Answer 13

Person’s rho

Question 14

Merits of Person’s rho

Answer 14

Advantages
Value unchanged under operation of strictly increasing linear transformations
ρ(a+bX,c+dY)=ρ(X,Y) where b and d>0

Disadvantages
Value not unchanged under operation of strictly non-linear increasing transformations
Not well defined where variances are infinte so can’t be used for some heavy-tailed distributions
Independent variables are uncorrelated, r(x,y) = 0, but not all uncorrelated variables are independent (i.e. r(x,y) = 0 doesn’t imply independence just not linear relationship)
Pearson’s rho only valid correlation measure if marginals are jointly elliptical
Given marginals X and Y, and specified rho, won’t necessarily be able to put together joint distribution to combine all info. Value of ro may be one that is unattainable, ie incompatible with marginal distributions**

Question 15

Name two rank correlation measures

Answer 15

• Kendall’s tau
• Spearman’s rho

Question 16

Properties of rank correlation measures

Answer 16

• Take values in interval [-1,1]
• Symmetric, i.e., τ(X,Y)= τ(Y,X) and ρ(X,Y)= sρ(Y,X)
• Give zero if RV are independent
• Take value of 1 if X and Y are co-monotonic (perfectly aligned) and -1 if counter monotonic (precisely in reverse)
• Rank correlation is preserved under non-linear, strictly increasing transormations
• 3/2 τ-1/2≤sρ≤1/2+τ-1/2 τ^2 if τ≥0
• 3/2 τ+1/2≥sρ≥-1/2+τ+1/2 τ^2 if τ≤0

Question 17

What is an advantage of rank correlation over linear

Answer 17

• Independent of marginal distributions which means it has more attractive properties

Question 18

Outline the features of deterministic models

Answer 18

• Uses set of predetermined assumptions
• Each set of assumptions determines value of each variable in model so output from model is fully determined
• Allow for prudence by adding margins

Question 19

List deterministic modelling approached

Answer 19

• Sensitivity analysis
• Scenario analysis
• Stress tests

Question 20

Outline how sensitivity analysis works

Answer 20

ary each input assumption one at a time to quantify the effect each has independently on the models output
* Can be done for every input or those that are key to the models operations
* Key limitation is no probabilities are attached to options used
* Keys an idea to the sensitivity of a set of results to changes in some inputs allowing some significant exposures to be recognized
* Variables hardly change individually in the real world hence we need scenario testing

Question 21

Advantages of sensitivity analysis

Answer 21

1. Develop understanding of risks faced
2. Provide insight into dependence of output on subjective assumptions
3. Satisfy supervisory authority’s requirements

Question 22

Limitations of sensitivity analysis

Answer 22

Doesn’t consider probabilities of changes in parameters

Question 23

Outline scenario analysis

Answer 23

• Change multiple inputs simultaneously.
• Scenario: set of model inputs representing a plausible and internally consistent set of future conditions
• Assess impact of financial and emerging risks

Question 24

How would you use scenario analysis within RM framework

Answer 24

1. Decide on the scenarios to test. Can be based on past or asking people what they think the worst case is
2. Establish the impact on risk factors/model inputs - set up inputs in a such a way that the worst case scenario chosen in 1 is achieved
3. Take action based on results. Put plans in place to minimize the effect of the scenario
4. Once risk responses are included, do scenario analysis again to see impact of the responses
5. Review scenarios to ensure they are still relevant over time as the business evolves

Question 25

Advantages of scenario analysis

Answer 25

• It facilitates the evaluation of the potential impact of plausible future events
• Provides useful info to supplement traditional models based on statistical info
• Can facilitate the production of action plans to deal with possible future catastrophes
• Helps when there is limited data to build a complex stochastic model. Usually for new risks
• Regulators can use this to compare a range of consistent scenarios across firms
• For extreme events where probabilities obtain may be unreliable, this method is a good alternative

Question 26

Disadvantages of scenario analysis

Answer 26

• Can be a complex process
• Reliance of generating appropriate hypothetical extreme events
• Have we considered all the scenarios?
• Does not allow for probabilities for each scenario so from a risk control perspective we may not be able to assess the cost vs benefit of the control
• You can consider only the bad scenarios and set risk responses for those but the problem is that these responses may not be appropriate for upside risks