Shapland Flashcards
1
Q
what does reserving tend to focus on (as an answer)?
Shapland
A
point estimates rather than distributions of reserves
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
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
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
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
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
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
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
9
Q
what does sampling with replacement assume about residuals?
Shapland
A
assumes they are independent and identically distributed
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
11
Q
why is the ODP bootstrap model sometimes referred to as “semi-parametric”?
(Shapland)
A
-we are not parameterizing the residuals
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
13
Q
why might we multiply the Pearson residuals by f^DoF up front?
(Shapland)
A
to correct for bias in the residuals
14
Q
what are Pearson residuals * f^DoF known as?
Shapland
A
scaled Pearson residuals
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)
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
17
Q
how is the hat matrix viewed, compared to the degrees of freedom factor?
(Shapland)
A
replacement for AND improvement over DoF factor
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
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
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
21
Q
what does the distribution of possible outcomes represent when the ODP bootstrapping model is applied to incurred data?
(Shapland)
A
represents IBNR
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
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
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)
25
how do we apply Approach 2 for modeling an unpaid loss distr. using incurred data?
(Shapland)
-apply ODP bootstrap to the Munich CL (MCL) model
26
how does the Munich Chain Ladder model predict ultimate losses?
(Shapland)
- 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
27
what are two advantages of Approach 2 over Approach 1? (for modeling an unpaid loss distr. using incurred data)
(Shapland)
- doesn't require us to model paid losses twice
| - explicitly measures correlation between paid and incurred losses
28
what is an issues with using the ODP bootstrap procces?
| Shapland
iterations for latest few AY tend to be more variable than what we would expect, given the simulations from earlier AY
29
why do ODP boostrap iterations for latest few AY tend to be more variable than what we'd expect?
(Shapland)
-more age-to-age factors are used to extrapolate sampled values to develop point estimates for each iteration
30
how do we fix the issue that latest few AY tend to be more variable than expected when using the ODP boostrap process?
(Shapland)
- can extrapolate future incremental values using the BF or CC methods
- can make these methods stochastic by converting deterministic assumptions to stochastic assumptions
31
what are two drawbacks to the GLM bootstrap model?
| Shapland
- 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
32
what are four benefits to the GLM bootstrap model?
| Shapland
- 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
33
what is an issue with adding a CY trend to the GLM bootstrap model, and how do we deal with it?
(Shapland)
- 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
34
what is an example of matching the GLM bootstrap model parameters to statistical features found in the data?
(Shapland)
- 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
35
how do we produce point estimates using the GLM bootstrap model?
(Shapland)
-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
36
what is one drawback of the using the GLM boostrap model to produce point estimates?
(Shapland)
-additional time is required to fit a GLM to each sample triangle
37
what are three options for dealing with extreme outcomes?
| Shapland
- identify the extreme iterations and remove them
- recalibrate the model
- limit incremental losses to zero
38
when removing extreme iterations, what do we need to be careful about?
(Shapland)
be careful to only remove unreasonable extreme iterations so that the probability is not understated
39
how would we go about recalibrating a model to deal with extreme iterations?
(Shapland)
- 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)
40
what does it mean to limit incremental losses to zero in dealing with extreme outcomes?
(Shapland)
- 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
41
what is an argument in favor of adjusting residuals s.t. their average is zero?
(Shapland)
- 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
42
what is an argument against adjusting residuals to a zero average?
(Shapland)
-non-zero average of residuals is a characteristic of the data set, so they shouldn't be adjusted
43
what is a method to adjust for a non-zero sum of residuals?
| Shapland
add a single constant to all residuals s.t. sum of shifted residuals is zero
44
in the GLM bootstrap, how would we go about using an L-year weighted average?
(Shapland)
- 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
45
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)
- GLM models incremental claims directly, can be parameterized using a trapezoid
- each parameter set is used to project the sample triangles to ultimate
46
how do we use an L-year weighted average with the ODP bootstrap?
(Shapland)
- 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
47
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)
- 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
48
what calculations are affected by missing values from the loss triangle?
(Shapland)
- LDFs
- fitted triangle (if missing value lies on last diagonal)
- residuals
- degrees of freedom
49
what are approaches to managing missing values in the ODP bootstrap model?
(Shapland)
- 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
50
what is a consequence of excluding missing values when using the ODP bootstrap model?
(Shapland)
- 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)
51
what happens when there are missing values, when we are using the GLM bootstrap model?
(Shapland)
- missing data reduces number of observations used in model
| - could use a method from ODP bootstrap model to estimate missing data if desired
52
what are two approaches to managing outliers when using the ODP bootstrap model?
(Shapland)
- 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
53
what is the idea behind excluding outliers in residual/LDF calcs, but including during sample triangle projection process?
(Shapland)
-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
54
what are three ways to exclude outliers when calculating age-to-age factors?
(Shapland)
- exclude in numerator
- exclude in denominator
- exclude in numerator
55
how are outliers treated when using the GLM bootstrap model?
| Shapland
-treated similarly to missing data: if considered not representative of real variability, outlier should be excluded and model shoild be parameterized without it
56
what might a significant number of outliers indicate?
| Shapland
model may be a poor fit to the data
57
what might we do if there are a significant number of outliers when using the GLM bootstrap?
(Shapland)
-new parameters could be chosen
OR
-distribution of error (z param) could be changed
58
what might we do if there are a significant number of outliers when using the ODP bootstrap?
(Shapland)
-an L-year wtd avg may be used to provide a better model fit
59
what might a large number of outliers mean for the ODP bootstrap and why?
(Shapland)
-may just mean that residuals are highly skewed because ODP bootstrap doesn't require a specific distribution for residuals)
60
if residuals are highly skewed, what action should be taken when using the ODP bootstrap model?
(Shapland)
-outliers should be included in fitting process to replicate true nature of the residuals
61
what is homoscedasticity?
| Shapland
-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
what residual behavior implies homoscedasticity?
| Shapland
-standardized residuals in some dev. periods appear to be more variable than standardized residuals in other periods
63
what is heteroscedasticity?
| Shapland
when model errors do not share a common variance
64
what are three options when adjusting for heteroscedasticity?
(Shapland)
- stratified sampling
- calculating variance params
- calculating scale params
65
how do we use stratified sampling to adjust for heteroscedasticity?
(Shapland)
- group dev. periods with homogeneous variances
| - sample with replacement from residuals in each group separately
66
what is an advantage of using stratified sampling to adjust for heteroscedasticity?
(Shapland)
straightforward and easy to implement
67
what is a disadvantage of using stratified sampling to adjust for heteroscedasticity?
(Shapland)
-some groups may only have a few residuals in them -> limits variability in possible outcomes
68
how do we use variance params to adjust for heteroscedasticity?
(Shapland)
- 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
what is a problem with using variance params to adjust for heteroscedasticity, and how do we fix it?
(Shapland)
- alters original distribution of residuals
| - fix by dividing resampled residuals by corresponding hetero-adjustment factor
70
how do we calculate scale parameters to adjust for heteroscedasticity?
(Shapland)
- 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
how many parameters (i.e. p value) are used in calculating scale & hetero-adjustment factors?
(Shapland)
general, need to include the number of hetero groups - 1
| one of the factors could be rebased to 1
72
is using hetero-adjustment factors based on scale parameters or variances better?
(Shapland)
- technically scale parameters is more theoretically sound
| - practical difference between the options is often negligible
73
what does the ODP bootstrap model require re: shape and exposures?
(Shapland)
- symmetrical shape
| - homoecthesious data
74
what does "symmetrical shape" mean, as required by the ODP bootstrap model?
(Shapland)
-i.e. annual by annual, quarterly by quarterly, etc.
75
what does "homoecthesious data" mean?
| Shapland
-similar exposures
76
how can we relax the ODP bootstrap model's requirement for symmetrical shape?
(Shapland)
-using L-year weighted average or excluding the first few diagonals
77
what does heteroecthesious data refer to?
| Shapland
incomplete or uneven exposures at interim evaluation dates
78
what are the two most common types of heteroecthesious data triangles?
(Shapland)
- "partial first development period" triangles
| - "partial last calendar period" triangles
79
when does partial first development period data occur, and what is an example?
(Shapland)
- 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
is partial first development period data a problem for parameterizing an ODP bootstrap model, and why?
(Shapland)
not a problem - Pearson residuals use the square root of the fitted value to make them all "exposure independent"
81
for what calculations do we need an adjustment for partial first development period data, with the ODP model (or deterministic analysis)?
(Shapland)
-when projecting future incremental values - must reduce projected future values by half to remove the extra exposures (before or after simulating process variance)
82
when does partial last calendar period data occur, and what is an example of it?
(Shapland)
- 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
how would a deterministic analysis deal with partial last calendar year data?
(Shapland)
- 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
what adjustments must we make when parameterizing the ODP bootstrap model with partial last calendar period data?
(Shapland)
- 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
what adjustments must we make during the ODP bootstrap simulation process when using partial last calendar period data?
(Shapland)
- 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
what is a common issue in real data? (and examples)
| Shapland
- exposures have changed dramatically over the years
| - ex: rapid growth or run-off
87
how do we adjust for changing exposures under the ODP bootstrap model?
(Shapland)
- 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
how do we adjust for changing exposures under the GLM bootstrap model?
(Shapland)
-GLM model is fit to exposure-adjusted losses (similar to ODP bootstrap model)
89
what is the primary difference with exposure adjustments in the ODP and GLM bootstrap models?
(Shapland)
-exposure adjusted losses with HIGHER exposures are assumed to have LOWER variance when fitting the GLM
90
how might exposure adjustments affect parameterization of the GLM bootstrap model?
(Shapland)
-could allow fewer AY parameters for GLM bootstrap model
91
what is a rule of thumb for using a tail factor with the ODP bootstrap model?
(Shapland)
tail factor standard deviation is 50% or less of the tail factor, minus 1
92
how do we implement a tail factor in the GLM bootstrap model?
(Shapland)
- 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
what might we do if we believe that extreme observations are NOT captured well in the ODP bootstrap loss triangle?
(Shapland)
parameterize a distribution for the residuals (e.g. normal) and resample using the distribution
94
what are three purposes for diagnostic tools to assess the quality of a stochastic model?
(Shapland)
- test various assumptions in the model
- gauge the quality of the model fit
- guide the adjustment of model parameters
95
what is the goal of diagnostic testing of stochastic models?
| Shapland
-find a set of reasonable models that provide the most realistic and consistent simulations
96
what are residual graphs intended to test?
| Shapland
test assumption that residuals are independent and identically distributed
97
what can we graph residuals by/against?
| Shapland
- development period, accident period, calendar period
| - fitted incremental loss
98
what do we examine in residual graphs?
| Shapland
- are there any trends exhibited (should have random pattern)
- heteroscedasticity - do residuals have different variances?
99
how might we visualize how to group heteroscedastic residuals?
(Shapland)
graph relative standard deviations and look for natural groupings
100
why is it helpful to run a normality test on ODP residuals?
| Shapland
-although ODP model doesn't require residuals to be normally distributed, can compare parameter sets and assess skewness of residuals
101
what p-value would indicate normally-distributed residuals?
| Shapland
p-value should be large (>5%)
102
what R^2 value would indicate normally-distributed residuals?
(Shapland)
-R^2 should be close to 1
103
what is a shortcoming of the p-value and R^2 tests, and how might we address this limitation?
(Shapland)
fail to adjust (or penalize) for number of parameters used in the model
-use AIC and BIC
104
what AIC/BIC values would indicate normally-distributed residuals?
(Shapland)
small AIC/BIC
105
how might we check if check if our heteroscedastic adjustments improved the fit of the model?
(Shapland)
-run normality plots and test values before and after adjustments
106
how might we identify outliers?
| Shapland
box-whisker plot
107
where do the whiskers of a box-whisker plot extend to?
| Shapland
extend to largest values within three times the inter-quartile range (25th to 75th percentile)
108
how are outliers identified with a box-whisker plot?
| Shapland
values beyond the whiskers are considered outliers, identified with a point
109
when do we want to remove outliers?
| Shapland
if outliers represent extreme events, NOT expected to happen again
110
when might we want to keep outliers in our model?
| Shapland
- 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
what does the principle of parsimony state?
| Shapland
a model with fewer parameters is preferred as long as the goodness of fit is not markedly different
112
based on a residual plot, when might we consider adding parameters to the GLM model?
(Shapland)
if residuals by accident period, dev. period, and calendar period are not randomly scattered around zero - consider adding params
113
when might we remove parameters from a GLM bootstrap model?
| Shapland
if certain params are not statistically significant
114
how do the implied development pattern graphs look for the ODP bootstrap model vs. the optimal GLM bootstrap model?
(Shapland)
-optimal GLM model produces dev patterns that is a smoothed version of ODP pattern, but still achieves overall shape
115
what should be reviewed after diagnostics?
| Shapland
descriptive statistics (mean, percentiles, s.d.) relating to simulations
116
how should standard error of the estimated-unpaid losses change over time & why?
(Shapland)
standard error should increase when moving from oldest years to most recent years - because s.e. follows magnitude of the results
117
how should the total standard error compare to any individual standard error?
(Shapland)
total s.e. should be larger than any individual s.e.
118
how should coefficient of variation move from oldest years to most recent years & why?
(Shapland)
- 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
what issues might cause the coefficient of variation to rise in the most recent years?
(Shapland)
- 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
how should the total coefficient of variation compare to any individual year's coefficient of variation?
(Shapland)
total coefficient of variation should be smaller than any individual year's coefficient of variation
121
how will the s.e. or CoV for all years combined compare to the sum of s.e. or CoV for individual years?
(Shapland)
all years combined < sum of all individual years
-true of all models, even unreasonable ones
122
how does reviewing mean and s.d. of incremental values help diagnostically?
(Shapland)
-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
what are two methods for combining the results of multiple models?
(Shapland)
- run models witht he same random variables (e.g. same random residuals in terms of position)
- run models with independent random variables
124
when running models with the same random variables, at what point are the results combined?
(Shapland)
-incremental values for each model are weighted together for each iteration by AY
125
when running models with independent random variables, how are the results combined?
(Shapland)
- 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
what are ways to address model results of negative IBNR that conflicts with case reserves?
(Shapland)
- 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
what distributions might we fit to total unpaid claim distributions (after model results have been combined and tabulated)?
(Shapland)
-can fit lognormal, nromal, gamma distributions
128
what can we used smoothed results of bootstrap models for?
| Shapland
- assess quality of fit
- parameterize a dynamic financial analysis (DFA) model
- estimate extreme values
- estimate TVaR
129
what is a benefit of using smoothed bootstrap results?
| Shapland
some of the random noise is prevented from distorting the calculations of specific metrics
130
what does it mean to "estimate cash flows"?
| Shapland
review model results by future calendar year
131
what is the main difference in unpaid calendar year vs. accident year?
(Shapland)
standard errors and coefficients of variations move in opposite directions
132
what direction do s.e. and CoV move for CY vs. AY unpaid claims?
(Shapland)
- 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
why do CY unpaid claim SE and CoV move in the directions they do?
(Shapland)
- further in future, CY unpaid claim estimates will decrease -> decrease in absolute SE
- relative to its mean, the variability increases substantially
134
how are estimated ultimate loss ratios by AY calculated?
| Shapland
-use all simulated values, not just values beyond end of historical triangle
135
if only interested in future volatility of loss ratios, what might we do?
(Shapland)
-add estimated unpaid claim estimates to actual cumulative paid values and divide by premiums
136
what would CoV for estimated ultimate loss ratio look like across accident yeras?
(Shapland)
-should be fairly constant because standard errors should be proportional to the main
137
what might an increasing coefficient of variation for estimated ultimate loss ratios indicate?
(Shapland)
large parameter uncertainty (same as in estimated unpaid)
138
what are three ways we could aggregate estimates to the business unit level?
(Shapland)
(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
what is an issue with using a multivariate distribution to aggregate ODP boostrap results to the business unit level?
(Shapland)
- requires us to know the distribution of each business segment
- ODP boostrap doesn't assume a specific distribution
140
how does location mapping work (for combining business unit estimates)?
(Shapland)
use residuals from same location in respective triangles - preserves correlation of original residuals in the sampling process
141
what are benefits of the location mapping approach?
| Shapland
- can be easily implemented in a spreadsheet
| - doesn't require us to estimate a correlation matrix
142
what are drawbacks of location mapping?
| Shapland
- 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
how does re-sorting work (for combining business unit estimates)?
(Shapland)
- 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
what are benefits of the re-sorting method?
| Shapland
- 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
what approximation to reserve risk correlation is made when estimating correlation with residuals?
(Shapland)
- 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
what approximation to pricing risk correlation is made when estimating correlation with residuals?
(Shapland)
- 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
how do we truly validate a model?
| Shapland
compare actual outcomes to modeled outcomes
148
using percentiles, how do we gauge if a model is working well?
(Shapland)
- 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
how did the Mack model test against the 99th percentile, and what does this imply?
(Shapland)
- actual results exceeded the estimated 99th percentile 8-13% of the time
- implies the Mack model underestimates tail events
150
how did the ODP bootstrap model compare (to Mack) in tests against the 99th percentile?
(Shapland)
- also underestimated tail events
| - performed stronger than the Mack model
151
what are four future research avenues (re: ODP bootstrap model)?
(Shapland)
- 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
