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exam 7 > Shapland > Flashcards

Shapland Flashcards

1
Q

what does reserving tend to focus on (as an answer)?

Shapland

A

point estimates rather than distributions of reserves

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2
Q

why is the reserving focus beginning to change?

Shapland

A
  • SEC requesting more reserving risk info from publicly traded companies
  • rating agencies are building dynamic risk models to help rate insurers - ask for input from company actuaries re: reserve distr
  • companies start to use dynamic risk models in internal risk management
  • Solvency II regulations in Europe emphasize unpaid claim distributions
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3
Q

what are two assumptions that can be made to create the bootstrap model that reproduces the CL model?

(Shapland)

A
  • assume each AY has same dev. factor

- assume each AY has a parameter representing its relative level

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4
Q

what do the CL, BF and CC assume about homogeneity of AY?

Shapland

A
  • CL assumes AY are NOT homogeneous

- BF and CC assume some homogeneity by incorporating future expected results into reserve estimate

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5
Q

for the error distribution of an ODP model, what z values represent which distributions?

(Shapland)

A

z=0 : Normal
z=1 : ODP
z=2 : Gamma
z=3 : Inverse Gaussian

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6
Q

what is one important property of the over-dispersed Poisson model?

(Shapland)

A

fitted incremental claims will exactly equal the fitted incremental claims derived using the standard CL factors

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7
Q

what are three important consequences of the fact that the ODP incr fitted claims match the CL method?

(Shapland)

A
  • simple LR algorithm can be used in place of more complicated GLM algorithm
  • use of age-to-age factors serves as a bridge to deterministic framework - more easily explain model
  • log link function doesn’t work for negative incr claims - link ratios remedies this issue
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8
Q

what types of residuals are used for the ODP model, and why?

Shapland

A

Pearson residuals are used - they are calculated consistently with the scale parameter, phi

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9
Q

what does sampling with replacement assume about residuals?

Shapland

A

assumes they are independent and identically distributed

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10
Q

what does sampling with replacement require about the distribution of residual,s and why is it an advantage?

(Shapland)

A

-does NOT require normal distribution -> distributional form of residuals will flow through the simulation process

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11
Q

why is the ODP bootstrap model sometimes referred to as “semi-parametric”?

(Shapland)

A

-we are not parameterizing the residuals

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12
Q

why do England & Verrall say the distribution of points (in the sample triangles from residuals) should be multiplied by a D.o.F adjustment factor?

(Shapland)

A

-allow for over-dispersion of the residuals in the sampling process
AND
-add process variance to obtain a distribution of possible outcomes

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13
Q

why might we multiply the Pearson residuals by f^DoF up front?

(Shapland)

A

to correct for bias in the residuals

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14
Q

what are Pearson residuals * f^DoF known as?

Shapland

A

scaled Pearson residuals

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15
Q

does the degrees of freedom bias correction create standardized residuals, and why is it important?

(Shapland)

A

NO - important because standardized residuals ensure that each residual has the same variance (assuming model fit to data is properly specified)

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16
Q

if heteroscedasticity exists within the Pearson residuals, what might it indicate?

(Shapland)

A
  • could indicate that something other than a Poisson distribution should be used
  • might mean we need more predictors
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17
Q

how is the hat matrix viewed, compared to the degrees of freedom factor?

(Shapland)

A

replacement for AND improvement over DoF factor

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18
Q

what do we assume about each future incremental claim (m_w,d), in order to include process variance?

(Shapland)

A
  • assume each future incremental claim, m_w,d is the mean of a gamma distr
  • assume that phi*m_w,d is the variance of a gamma distribution
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19
Q

what type of residuals do we exclude when sampling, and why?

Shapland

A

-exclude zero-value residuals, because those cells contain variance - we just don’t know what it is yet

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20
Q

what does the distribution of possible outcomes represent when the ODP bootstrapping model is applied to paid data?

(Shapland)

A

represents total unpaid claims

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21
Q

what does the distribution of possible outcomes represent when the ODP bootstrapping model is applied to incurred data?

(Shapland)

A

represents IBNR

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22
Q

how do we apply Approach 1 for modeling an unpaid loss distribution using incurred data?

(Shapland)

A
  • run paid data model in conjunction with incurred data model
  • use random pmt pattern from each iteration of the paid data model to convert ultimate values from each incurred model iteration to develop pd losses by AY
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23
Q

what is a benefit to Approach 1 for modeling an unpaid loss distr. using incurred data?

(Shapland)

A

allows us to use case reserves to help predict ultimate losses, while still focusing on pmt stream for measuring risk

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24
Q

what is an improvement to Approach 1 for modeling an unpaid loss distr. using incurred data?

(Shapland)

A

-inclusion of correlation between paid and incurred models (possibly in residual sampling process)

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25
Q

how do we apply Approach 2 for modeling an unpaid loss distr. using incurred data?

(Shapland)

A

-apply ODP bootstrap to the Munich CL (MCL) model

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26
Q

how does the Munich Chain Ladder model predict ultimate losses?

(Shapland)

A
  • uses inherent relationship/correlation between paid and incurred losses to predict ultimate losses
  • when paid losses are low relative to incurred losses, future paid loss dev. tends to be higher than average
  • when paid losses are high relative to incurred losses - future paid loss dev. tends to be lower than average
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27
Q

what are two advantages of Approach 2 over Approach 1? (for modeling an unpaid loss distr. using incurred data)

(Shapland)

A
  • doesn’t require us to model paid losses twice

- explicitly measures correlation between paid and incurred losses

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28
Q

what is an issues with using the ODP bootstrap procces?

Shapland

A

iterations for latest few AY tend to be more variable than what we would expect, given the simulations from earlier AY

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29
Q

why do ODP boostrap iterations for latest few AY tend to be more variable than what we’d expect?

(Shapland)

A

-more age-to-age factors are used to extrapolate sampled values to develop point estimates for each iteration

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30
Q

how do we fix the issue that latest few AY tend to be more variable than expected when using the ODP boostrap process?

(Shapland)

A
  • can extrapolate future incremental values using the BF or CC methods
  • can make these methods stochastic by converting deterministic assumptions to stochastic assumptions
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31
Q

what are two drawbacks to the GLM bootstrap model?

Shapland

A
  • GLM must be solved for each iteration of the bootstrap model -> may slow down simulation
  • model is no longer directly explainable to others using age-to-age factors
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32
Q

what are four benefits to the GLM bootstrap model?

Shapland

A
  • fewer parameters helps avoid over-parameterizing the model
  • ability to add params for CY trends
  • ability to model data shapes other than triangles
  • allows us to match the model params to the statistical features found in the data, and to extrapolate those features
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33
Q

what is an issue with adding a CY trend to the GLM bootstrap model, and how do we deal with it?

(Shapland)

A
  • system of equations no longer has a unique answer

- instead, start with a model with one parameter of alpha, beta, gamma each, remove and add as needed

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34
Q

what is an example of matching the GLM bootstrap model parameters to statistical features found in the data?

(Shapland)

A
  • modeling with fewer dev. trend parameters -> last parameter is assumed to continue past the end of the triangle
  • gives us a tail without specifying a tail factor
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35
Q

how do we produce point estimates using the GLM bootstrap model?

(Shapland)

A

-do NOT apply age-to-age factors to each sample triangle -> instead, fit same GLM model underlying residuals to each sample triangle, and use resulting params to produce ultimates and reserve point estimates

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36
Q

what is one drawback of the using the GLM boostrap model to produce point estimates?

(Shapland)

A

-additional time is required to fit a GLM to each sample triangle

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37
Q

what are three options for dealing with extreme outcomes?

Shapland

A
  • identify the extreme iterations and remove them
  • recalibrate the model
  • limit incremental losses to zero
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38
Q

when removing extreme iterations, what do we need to be careful about?

(Shapland)

A

be careful to only remove unreasonable extreme iterations so that the probability is not understated

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39
Q

how would we go about recalibrating a model to deal with extreme iterations?

(Shapland)

A
  • identify source of negative incremental losses and remove it if necessary, then reparameterize the model
  • alternatively, could create separate models (e.g. if salvage/sub. cause negative values, model them separately, and combine iterations)
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40
Q

what does it mean to limit incremental losses to zero in dealing with extreme outcomes?

(Shapland)

A
  • replace negative incrementals with zeros in original triangles, sampled triangles, OR projected future incremental losses
  • can also replace negative incr losses with zeroes based on their dev. column
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41
Q

what is an argument in favor of adjusting residuals s.t. their average is zero?

(Shapland)

A
  • if avg of residuals is positive, then re-sampling from the residuals will add variability to resampled incremental losses
  • may also cause resampled incremental losses to have an avg. greater than the fitted loss
  • in this respect, residuals should be adjusted
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42
Q

what is an argument against adjusting residuals to a zero average?

(Shapland)

A

-non-zero average of residuals is a characteristic of the data set, so they shouldn’t be adjusted

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43
Q

what is a method to adjust for a non-zero sum of residuals?

Shapland

A

add a single constant to all residuals s.t. sum of shifted residuals is zero

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44
Q

in the GLM bootstrap, how would we go about using an L-year weighted average?

(Shapland)

A
  • exclude first few diagonals in triangle (leaves us with L+1 included diagonals)
  • excluded diagonals are given 0 weight in model, fewer CY params are required
  • only sample residuals for trapezoid used to parameterize original model
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45
Q

when using an L-year weighted average with the GLM bootstrap, why do we only sample residuals for the trapezoid used to parameterize the original model?

(Shapland)

A
  • GLM models incremental claims directly, can be parameterized using a trapezoid
  • each parameter set is used to project the sample triangles to ultimate
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46
Q

how do we use an L-year weighted average with the ODP bootstrap?

(Shapland)

A
  • calculate L-year avg. factors instead of all-year factors
  • exclude first few diagonals when calculating residuals
  • still sample residuals for entire triangle when running bootstrap simulations
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47
Q

why do we still need to sample residuals for the entire triangle when using an L-year weighted average with the ODP bootstrap model?

(Shapland)

A
  • ODP boostrap requires cumulative values in order to calculate link ratios
  • once we have cumulative values for each sample triangle, we use -year avg factors to project sample triangles to ultimate
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48
Q

what calculations are affected by missing values from the loss triangle?

(Shapland)

A
  • LDFs
  • fitted triangle (if missing value lies on last diagonal)
  • residuals
  • degrees of freedom
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49
Q

what are approaches to managing missing values in the ODP bootstrap model?

(Shapland)

A
  • estimate missing value using surrounding values
  • exclude missing value when calculating LDFs
  • if missing value lies on last diagonal - estimate value OR use value in second-last diagonal to construct fitted triangle
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50
Q

what is a consequence of excluding missing values when using the ODP bootstrap model?

(Shapland)

A
  • no corresponding residual will be calculated for the missing value
  • must still sample for entire triangle so we can calculate cumulative values during simulation process
  • once sample triangles are calculated, exclude cells corresponding to missing values from the projection process (ie - when calculating LDFs)
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51
Q

what happens when there are missing values, when we are using the GLM bootstrap model?

(Shapland)

A
  • missing data reduces number of observations used in model

- could use a method from ODP bootstrap model to estimate missing data if desired

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52
Q

what are two approaches to managing outliers when using the ODP bootstrap model?

(Shapland)

A
  • exclude outliers completely (proceed in same manner as missing value)
  • exclude outliers when calculating age-to-age factors and residuals (similar to missing values),, but include outlier cells during sample projection process
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53
Q

what is the idea behind excluding outliers in residual/LDF calcs, but including during sample triangle projection process?

(Shapland)

A

-remove extreme impact of incremental cell by excluding outlier during the fitting process, while still including some non-extreme variability by including cell in sample triangle projection process

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54
Q

what are three ways to exclude outliers when calculating age-to-age factors?

(Shapland)

A
  • exclude in numerator
  • exclude in denominator
  • exclude in numerator
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55
Q

how are outliers treated when using the GLM bootstrap model?

Shapland

A

-treated similarly to missing data: if considered not representative of real variability, outlier should be excluded and model shoild be parameterized without it

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56
Q

what might a significant number of outliers indicate?

Shapland

A

model may be a poor fit to the data

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57
Q

what might we do if there are a significant number of outliers when using the GLM bootstrap?

(Shapland)

A

-new parameters could be chosen
OR
-distribution of error (z param) could be changed

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58
Q

what might we do if there are a significant number of outliers when using the ODP bootstrap?

(Shapland)

A

-an L-year wtd avg may be used to provide a better model fit

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59
Q

what might a large number of outliers mean for the ODP bootstrap and why?

(Shapland)

A

-may just mean that residuals are highly skewed because ODP bootstrap doesn’t require a specific distribution for residuals)

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60
Q

if residuals are highly skewed, what action should be taken when using the ODP bootstrap model?

(Shapland)

A

-outliers should be included in fitting process to replicate true nature of the residuals

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61
Q

what is homoscedasticity?

Shapland

A

-residuals are IID, can apply a residual from one dev./accident period to fitted loss in any other dev/accident period to produce sampled values

62
Q

what residual behavior implies homoscedasticity?

Shapland

A

-standardized residuals in some dev. periods appear to be more variable than standardized residuals in other periods

63
Q

what is heteroscedasticity?

Shapland

A

when model errors do not share a common variance

64
Q

what are three options when adjusting for heteroscedasticity?

(Shapland)

A
  • stratified sampling
  • calculating variance params
  • calculating scale params
65
Q

how do we use stratified sampling to adjust for heteroscedasticity?

(Shapland)

A
  • group dev. periods with homogeneous variances

- sample with replacement from residuals in each group separately

66
Q

what is an advantage of using stratified sampling to adjust for heteroscedasticity?

(Shapland)

A

straightforward and easy to implement

67
Q

what is a disadvantage of using stratified sampling to adjust for heteroscedasticity?

(Shapland)

A

-some groups may only have a few residuals in them -> limits variability in possible outcomes

68
Q

how do we use variance params to adjust for heteroscedasticity?

(Shapland)

A
  • group dev. periods with homogeneous variances
  • calculate hetero-adjustment factor, h_i for each group, based on variances
  • multiply all residuals by corresponding h_i
  • sample with replacement from among ALL residuals
  • divide hetero-adjustment factor
69
Q

what is a problem with using variance params to adjust for heteroscedasticity, and how do we fix it?

(Shapland)

A
  • alters original distribution of residuals

- fix by dividing resampled residuals by corresponding hetero-adjustment factor

70
Q

how do we calculate scale parameters to adjust for heteroscedasticity?

(Shapland)

A
  • gorup dev. periods with homogeneous variances
  • calculate hetero-adjustment factors based on scale parameters (NOT variances)
  • multiply all residuals by corresponding h_i
  • multiply all residuals by corresponding h_i
  • sample with replacement from among ALL residuals
  • divide hetero-adjustment factor
71
Q

how many parameters (i.e. p value) are used in calculating scale & hetero-adjustment factors?

(Shapland)

A

general, need to include the number of hetero groups - 1

one of the factors could be rebased to 1

72
Q

is using hetero-adjustment factors based on scale parameters or variances better?

(Shapland)

A
  • technically scale parameters is more theoretically sound

- practical difference between the options is often negligible

73
Q

what does the ODP bootstrap model require re: shape and exposures?

(Shapland)

A
  • symmetrical shape

- homoecthesious data

74
Q

what does “symmetrical shape” mean, as required by the ODP bootstrap model?

(Shapland)

A

-i.e. annual by annual, quarterly by quarterly, etc.

75
Q

what does “homoecthesious data” mean?

Shapland

A

-similar exposures

76
Q

how can we relax the ODP bootstrap model’s requirement for symmetrical shape?

(Shapland)

A

-using L-year weighted average or excluding the first few diagonals

77
Q

what does heteroecthesious data refer to?

Shapland

A

incomplete or uneven exposures at interim evaluation dates

78
Q

what are the two most common types of heteroecthesious data triangles?

(Shapland)

A
  • “partial first development period” triangles

- “partial last calendar period” triangles

79
Q

when does partial first development period data occur, and what is an example?

(Shapland)

A
  • occurs when first dev. column has a different exposure period than the rest of columns
  • ex: annual data ending as of 6/30 -> periods ending 6, 18, 30, etc. months
80
Q

is partial first development period data a problem for parameterizing an ODP bootstrap model, and why?

(Shapland)

A

not a problem - Pearson residuals use the square root of the fitted value to make them all “exposure independent”

81
Q

for what calculations do we need an adjustment for partial first development period data, with the ODP model (or deterministic analysis)?

(Shapland)

A

-when projecting future incremental values - must reduce projected future values by half to remove the extra exposures (before or after simulating process variance)

82
Q

when does partial last calendar period data occur, and what is an example of it?

(Shapland)

A
  • occurs when latest diagonal only has a six-month development period
  • ex: dev periods of 12, 24, 36 for all data in triangle except latest diagonal, which has dev. periods of 6, 18, 30, etc.
83
Q

how would a deterministic analysis deal with partial last calendar year data?

(Shapland)

A
  • exclude latest diagonal when calculating LDFs
  • interpolate LDFs for exposures in last diagonal
  • use interpolated factors to project future vales - must reduce future values for latest AY by half
84
Q

what adjustments must we make when parameterizing the ODP bootstrap model with partial last calendar period data?

(Shapland)

A
  • annualize exposures in last diagonal to make them consistent with the rest of the triangle
  • fitted triangle is calculated based on annualized triangle to obtain residuals
85
Q

what adjustments must we make during the ODP bootstrap simulation process when using partial last calendar period data?

(Shapland)

A
  • age-to-age factors calculated from annualized sample triangles and interpolated
  • latest diagonal in sample triangle is adjusted back to six-month period
  • cumulative values are multiplied by interpolated age-to-age factors to project future values (must reduce future values by half for latest AY)
86
Q

what is a common issue in real data? (and examples)

Shapland

A
  • exposures have changed dramatically over the years

- ex: rapid growth or run-off

87
Q

how do we adjust for changing exposures under the ODP bootstrap model?

(Shapland)

A
  • divide claim data by EE for each AY (normally improves model fit)
  • simulation run on adjusted data
  • after process variance step, multiply results by EE to restate them in terms of total values
88
Q

how do we adjust for changing exposures under the GLM bootstrap model?

(Shapland)

A

-GLM model is fit to exposure-adjusted losses (similar to ODP bootstrap model)

89
Q

what is the primary difference with exposure adjustments in the ODP and GLM bootstrap models?

(Shapland)

A

-exposure adjusted losses with HIGHER exposures are assumed to have LOWER variance when fitting the GLM

90
Q

how might exposure adjustments affect parameterization of the GLM bootstrap model?

(Shapland)

A

-could allow fewer AY parameters for GLM bootstrap model

91
Q

what is a rule of thumb for using a tail factor with the ODP bootstrap model?

(Shapland)

A

tail factor standard deviation is 50% or less of the tail factor, minus 1

92
Q

how do we implement a tail factor in the GLM bootstrap model?

(Shapland)

A
  • assume that final dev. period will continue to apply incrementally until its effect on incremental claims is negligible
  • if using dev. year and CY params - assume both continue past end of sample triangle until effects on future incremental claims are negligible
93
Q

what might we do if we believe that extreme observations are NOT captured well in the ODP bootstrap loss triangle?

(Shapland)

A

parameterize a distribution for the residuals (e.g. normal) and resample using the distribution

94
Q

what are three purposes for diagnostic tools to assess the quality of a stochastic model?

(Shapland)

A
  • test various assumptions in the model
  • gauge the quality of the model fit
  • guide the adjustment of model parameters
95
Q

what is the goal of diagnostic testing of stochastic models?

Shapland

A

-find a set of reasonable models that provide the most realistic and consistent simulations

96
Q

what are residual graphs intended to test?

Shapland

A

test assumption that residuals are independent and identically distributed

97
Q

what can we graph residuals by/against?

Shapland

A
  • development period, accident period, calendar period

- fitted incremental loss

98
Q

what do we examine in residual graphs?

Shapland

A
  • are there any trends exhibited (should have random pattern)
  • heteroscedasticity - do residuals have different variances?
99
Q

how might we visualize how to group heteroscedastic residuals?

(Shapland)

A

graph relative standard deviations and look for natural groupings

100
Q

why is it helpful to run a normality test on ODP residuals?

Shapland

A

-although ODP model doesn’t require residuals to be normally distributed, can compare parameter sets and assess skewness of residuals

101
Q

what p-value would indicate normally-distributed residuals?

Shapland

A

p-value should be large (>5%)

102
Q

what R^2 value would indicate normally-distributed residuals?

(Shapland)

A

-R^2 should be close to 1

103
Q

what is a shortcoming of the p-value and R^2 tests, and how might we address this limitation?

(Shapland)

A

fail to adjust (or penalize) for number of parameters used in the model
-use AIC and BIC

104
Q

what AIC/BIC values would indicate normally-distributed residuals?

(Shapland)

A

small AIC/BIC

105
Q

how might we check if check if our heteroscedastic adjustments improved the fit of the model?

(Shapland)

A

-run normality plots and test values before and after adjustments

106
Q

how might we identify outliers?

Shapland

A

box-whisker plot

107
Q

where do the whiskers of a box-whisker plot extend to?

Shapland

A

extend to largest values within three times the inter-quartile range (25th to 75th percentile)

108
Q

how are outliers identified with a box-whisker plot?

Shapland

A

values beyond the whiskers are considered outliers, identified with a point

109
Q

when do we want to remove outliers?

Shapland

A

if outliers represent extreme events, NOT expected to happen again

110
Q

when might we want to keep outliers in our model?

Shapland

A
  • outliers represent extreme events that could happen again

- residuals are not normally distributed, so outliers are more common -> representative of the shape of the data

111
Q

what does the principle of parsimony state?

Shapland

A

a model with fewer parameters is preferred as long as the goodness of fit is not markedly different

112
Q

based on a residual plot, when might we consider adding parameters to the GLM model?

(Shapland)

A

if residuals by accident period, dev. period, and calendar period are not randomly scattered around zero - consider adding params

113
Q

when might we remove parameters from a GLM bootstrap model?

Shapland

A

if certain params are not statistically significant

114
Q

how do the implied development pattern graphs look for the ODP bootstrap model vs. the optimal GLM bootstrap model?

(Shapland)

A

-optimal GLM model produces dev patterns that is a smoothed version of ODP pattern, but still achieves overall shape

115
Q

what should be reviewed after diagnostics?

Shapland

A

descriptive statistics (mean, percentiles, s.d.) relating to simulations

116
Q

how should standard error of the estimated-unpaid losses change over time & why?

(Shapland)

A

standard error should increase when moving from oldest years to most recent years - because s.e. follows magnitude of the results

117
Q

how should the total standard error compare to any individual standard error?

(Shapland)

A

total s.e. should be larger than any individual s.e.

118
Q

how should coefficient of variation move from oldest years to most recent years & why?

(Shapland)

A
  • should generally decrease
  • older years have fewer pmts remaining, causing all of the variability to be reflected in the coefficient - but more recent years, random variations in remaining pmts tend to offset each other, reducing overall variability
119
Q

what issues might cause the coefficient of variation to rise in the most recent years?

(Shapland)

A
  • with increasing # params, parameter uncertainty increases when moving from oldest to most recent years - may overpower process uncertainty, causing an increase in variability
  • model may be overestimating the variability in most recent years - BF of CC may be better choice
120
Q

how should the total coefficient of variation compare to any individual year’s coefficient of variation?

(Shapland)

A

total coefficient of variation should be smaller than any individual year’s coefficient of variation

121
Q

how will the s.e. or CoV for all years combined compare to the sum of s.e. or CoV for individual years?

(Shapland)

A

all years combined < sum of all individual years

-true of all models, even unreasonable ones

122
Q

how does reviewing mean and s.d. of incremental values help diagnostically?

(Shapland)

A

-can view over time to identify inconsistencies - help to explain any coefficient of variation issues (is it the mean or the s.d. causing it?)

123
Q

what are two methods for combining the results of multiple models?

(Shapland)

A
  • run models witht he same random variables (e.g. same random residuals in terms of position)
  • run models with independent random variables
124
Q

when running models with the same random variables, at what point are the results combined?

(Shapland)

A

-incremental values for each model are weighted together for each iteration by AY

125
Q

when running models with independent random variables, how are the results combined?

(Shapland)

A
  • after running model, weights are used to select a model by randomly sampling the specified percentage of iterations from each model
    e. g.: 1000 iterations run for two models, weights = 25/75, sample 250 iterations from first model, 750 iterations from other model
126
Q

what are ways to address model results of negative IBNR that conflicts with case reserves?

(Shapland)

A
  • can shift weighted distributions
  • add fixed amt to AY to produce positive IBNR (if shape and width of distr. are believed to be appropriate)
  • multiply results by a factor (adjust just width, keep shape of model)
127
Q

what distributions might we fit to total unpaid claim distributions (after model results have been combined and tabulated)?

(Shapland)

A

-can fit lognormal, nromal, gamma distributions

128
Q

what can we used smoothed results of bootstrap models for?

Shapland

A
  • assess quality of fit
  • parameterize a dynamic financial analysis (DFA) model
  • estimate extreme values
  • estimate TVaR
129
Q

what is a benefit of using smoothed bootstrap results?

Shapland

A

some of the random noise is prevented from distorting the calculations of specific metrics

130
Q

what does it mean to “estimate cash flows”?

Shapland

A

review model results by future calendar year

131
Q

what is the main difference in unpaid calendar year vs. accident year?

(Shapland)

A

standard errors and coefficients of variations move in opposite directions

132
Q

what direction do s.e. and CoV move for CY vs. AY unpaid claims?

(Shapland)

A
  • CY: SE decrease and CoV increase as we move further into future
  • AY: SE increase and CoV decrease as we move further into future
133
Q

why do CY unpaid claim SE and CoV move in the directions they do?

(Shapland)

A
  • further in future, CY unpaid claim estimates will decrease -> decrease in absolute SE
  • relative to its mean, the variability increases substantially
134
Q

how are estimated ultimate loss ratios by AY calculated?

Shapland

A

-use all simulated values, not just values beyond end of historical triangle

135
Q

if only interested in future volatility of loss ratios, what might we do?

(Shapland)

A

-add estimated unpaid claim estimates to actual cumulative paid values and divide by premiums

136
Q

what would CoV for estimated ultimate loss ratio look like across accident yeras?

(Shapland)

A

-should be fairly constant because standard errors should be proportional to the main

137
Q

what might an increasing coefficient of variation for estimated ultimate loss ratios indicate?

(Shapland)

A

large parameter uncertainty (same as in estimated unpaid)

138
Q

what are three ways we could aggregate estimates to the business unit level?

(Shapland)

A

(can’t simply be added - segments tend to be correlated)

  • use a multivariate distribution whose parameters and correlations have been specified
  • location mapping
  • re-sorting
139
Q

what is an issue with using a multivariate distribution to aggregate ODP boostrap results to the business unit level?

(Shapland)

A
  • requires us to know the distribution of each business segment
  • ODP boostrap doesn’t assume a specific distribution
140
Q

how does location mapping work (for combining business unit estimates)?

(Shapland)

A

use residuals from same location in respective triangles - preserves correlation of original residuals in the sampling process

141
Q

what are benefits of the location mapping approach?

Shapland

A
  • can be easily implemented in a spreadsheet

- doesn’t require us to estimate a correlation matrix

142
Q

what are drawbacks of location mapping?

Shapland

A
  • requires all business units to have residual triangles that are the same size and have no missing values/outliers
  • does not allow any other correlation assumptions for stress testing purposes
143
Q

how does re-sorting work (for combining business unit estimates)?

(Shapland)

A
  • residuals are re-sorted until rank correlation between each business unit matches the desired correlation (as specified by a desired correlation matrix)
  • can calculate p-values for each correlation coefficient to test its significance
144
Q

what are benefits of the re-sorting method?

Shapland

A
  • residual triangles may have different shapes/sizes
  • different correlation assumptions may be employed
  • different correlation algorithms may have beneficial impacts on the aggregate distribution
145
Q

what approximation to reserve risk correlation is made when estimating correlation with residuals?

(Shapland)

A
  • reserve risk: correlation is between total unpaid amts for two segments
  • residuals: correlation is between each incremental future loss amt
  • may or may not be reasonable approximation
146
Q

what approximation to pricing risk correlation is made when estimating correlation with residuals?

(Shapland)

A
  • pricing risk: correlation is between loss ratio movements by AY between two segments - not expected to be close to zero
  • residuals: tends to result in correlations close to zero
  • may need alternative correlation assumptions for pricing risk
147
Q

how do we truly validate a model?

Shapland

A

compare actual outcomes to modeled outcomes

148
Q

using percentiles, how do we gauge if a model is working well?

(Shapland)

A
  • actual results should exceed the estimated percentiles “one minus the percentile” of the time
    e. g.: for 99th percentile, actual results should exceed the estimated 1% of the time
149
Q

how did the Mack model test against the 99th percentile, and what does this imply?

(Shapland)

A
  • actual results exceeded the estimated 99th percentile 8-13% of the time
  • implies the Mack model underestimates tail events
150
Q

how did the ODP bootstrap model compare (to Mack) in tests against the 99th percentile?

(Shapland)

A
  • also underestimated tail events

- performed stronger than the Mack model

151
Q

what are four future research avenues (re: ODP bootstrap model)?

(Shapland)

A
  • expand testing of ODP bootstrap with realistic (not artificial/perfect) data
  • expand ODP bootstrap model to incorporate Munich CL method
  • research other ways to use model in ERM
  • research how to use model for Solvency II requirements
  • research how to better estimate the correlation matrix

exam 7 (21 decks)

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