ERA 3 TIA Flashcards

1
Q

When implementing an Internal Risk Model, firms often underestimate? (3)

A
  • Resource Commitment - Staff, Systems, Software
  • Timelines
  • Organization impact
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2
Q

When implementing an Internal Risk Model - Staff Considerations (5)

A
  • Reporting Lines should be clear
  • Leader should have a reputation for Fairness
  • Functions Represented: U/W, Planning, Finance, Actuarial, Risk
  • Full Time Staff vs. Part Time Staff (also have day to day job)
  • Permanent Staff vs. Temporary Staff (for implementation)
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3
Q

Implementing IRM - Scope considerations? (4)

A
  • Underwriting Year
  • Reserves
  • Assets
  • Low Detail on Company OR High Detail on pilot segment
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4
Q

Parameter Estimation is difficult because (4):

A
  • Low Data Quality
  • Low Data Volume
  • Unique Characteristics of Firm
  • Differing Risk Attitudes
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5
Q

Correlation Assessment in an IRM is difficult because (4):

A
  • Lack of Data
  • High Political Sensitivity
  • spans Multiple Business Units
  • Significant impact on Company Risk Profile and Capital Allocation

IRM team recommends correlation assumptions
Owned by CRO/CEO/CUO

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6
Q

Why is Validation of an Internal Risk Model difficult?
How can we Validate?

A
  • No current model to compare to
  • Review a series of Complementary variables over an
    extended period
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7
Q

How should a Pilot Test be done for the
implementation of an Internal Risk Model?

A
  • Provide output in parallel to current decision metrics
    (allows user to get comfortable with new metrics)
  • High Level of the Company OR Detail of a Pilot Segment
  • Provide Education on New Metrics
  • Each Quarter increase Weight that is given to new metrics
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8
Q

Recommendations for Integration and Maintentance
of an Internal Risk Model (4)

A
  • Integrate into the Corporate Calendar that already exists
  • Major Updates - no more than twice a year
  • Minor Updates - via scaling
  • Input/Output - Ownership and Control must be very clear
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9
Q

Formula for Coefficient of Variation (CV) of Losses

A
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10
Q

What is Superimposed Inflation?

A

Severity Trend less General Inflation

[Claim Severity Trend] =
[General Inflation] + [Superimposed Inflation]

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11
Q

For Projecting Annual Loss Trend, the author
recommends an AR(1) process with what parameters?

A
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12
Q

What is the preferred method to estimate parameters
for Frequency and Severity Distributions?

A

Maximum Likelihood Estimator (MLE)

Among Unbiased estimators, it has the lowest Estimation
Error (for large data sets)

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13
Q

When Estimating Parameters how we can estimate
correlations?

A
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14
Q

How do the authors recommend we model parameter
estimates and their dependencies?

A

Model the parameter estimates as Joint LogNormal
with correlations from the Information Matrix

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15
Q

Why do we prefer to use Joint LogNormal to model
estimates of parameters? (2)

A
  • Removes Negative Values from possible
    simulated values
  • Parameter Estimates have a heavy tail -
    LogNormal captures this
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16
Q

What is Model Risk?

A

Risk that the selected model is not the correct one

17
Q

When estimating parameters - we can calculate the
Likelihood of the data given the selected parameters

What does the slope of the Negative Log Likelihood
tell us about our estimate of the parameters?

A

A steep slope tells us we are quite certain of our estimate of
the parameters

A shallow slope tells us we are not certain of our estimate of
the parameters

18
Q

A method to account for Model Risk

A
  • When comparing different models use the HQIC to
    compare them
  • Hannan-Quinn Information Criterion (HQIC) is a
    compromise on the # of parameters penalty
  • Multiple models can be chosen for a pool of possible
    models
  • For each simulation, draw one of these models, and then
    parameters from that model
19
Q

Formula for Copula Density

20
Q

How can we interpret the values of the copula density
c(u, v)?

A

If c(u, v) = 1, then the density is the same as if u & v were independent

c(u, v) > 1 Density is higher
c(u, v) < 1 Density is lower

21
Q

Gumbel τ

A

τ = 1 - 1/a

22
Q

HRT τ

A

τ = 1 / (2a + 1)

23
Q

Frank τ

A

(Don’t need to memorize)

not closed form

24
Q

Normal τ

A

τ = 2 * arcsin(a) / pi

25
Formula for the Conditional Distribution of v|u
26
Method to simulate Frank’s Copula
* Draw u, p ∼ Uniform[0, 1] * set p = C1(u, v) * solve for v * (u, v) are drawn from Frank‘s copula
27
Method to simulate Normal Copula
* Draw x, y ∼ Normal(0, 1) -> invert e.g. if x = 0, then u = 0.5 * z = ax +√ (1 − a^2) · y * u = Φ^−1(x) & v = Φ^−1(z) * (u, v) are drawn from the Normal Copula
28
Method to simulate Gumbel Copula
*Draw p,r ∼ Uniform[0, 1] * Solve for s:
29
What is the Left Tail Concentration Function
L(z) = P(U < z|V < z) = C(z, z)/z Probability that U is small, given that V is small
30
What is the Right Tail Concentration Function
R(z) = P(U > z|V > z) = (1 − 2z + C(z, z))/(1 − z) Probability that U is large, given that V is large
31
Which of the 4 copulas has a Right Tail Concentration Function that approaches zero in the limit?
Normal & Frank
32
Which of the 4 copulas has the lightest left tail?
HRT
33
Which Copula has a heavy right tail; and a left tail density similar to Normal?
Gumbel
34
What copulas are available to model dependencies among multiple variables?
* t-copula * Normal
35
What advantages does the t-copula have over other copulas? (4)
* Can be strongly correlated in the tails - this is controlled by the n parameter * Can join multiple variables * Has density where one variable is high and the other is low * approaches the Normal copula for large n
36
What is the limit of J(z)?
lim J(z) = τ as z→1
37
How do we use J(z) to fit a copula?
* Graph the empirical J(z) * Compare to graphs of J(z) for possible copulas
38
The limit of χ(z)
lim χ(z) = R as z→1
39
How do we use χ(z) to fit a copula?
* Graph the empirical χ(z) * Compare to graphs of χ(z) for possible copulas