A Practical Approach to Financial Modeling
2010 IABA Annual Meeting
August 6 - 7, 2010
Jay Vadiveloo, PhD, FSA, MAAA,CFA
© 2010 Towers Watson. All rights reserved.

This presentation has been prepared solely for informational purposes and Towers Watson does not make any representation or warranty, either express or implied, as to the accuracy, completeness or reliability of the information contained in this presentation.
Your organization should consult its own counsel, tax, actuarial and financing advisors as to legal and other matters concerning any of the material presented herein.
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Actuarial valuation of insurance liabilities typically involves production –based, seriatim calculations.
Today’s insurance products include complex features with investment oriented characteristics that require stochastic modeling of market and interest rate performance.
Commercial actuarial software has been designed to handle large, complex stochastic modeling of insurance liabilities.
In most actuarial analyses, for both regulatory and management purposes, the focus is on the risk exposure at the tails (typically the 90th percentile and beyond).
Long run times and lack of a management tool for what-if, actionable analysis.
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Actuarial
Methods
 Scenario reduction
 Modeling/compression
Advantages
 Familiar and well-understood
Disadvantages
 Reduces accuracy
 Exposed to model risk
 Run-time savings not sufficient
Technological
Methods
 Grid processing
Advantages
 Brute force method so easy to understand
 Can always buy more computers
Disadvantages
 Costly
 Battle for grid time
 Still long run times
Market-driven
Methods
 Replicating portfolios towerswatson.com
Advantages
 Closed-form solutions so extremely fast
 Allows processing of many scenarios
Disadvantages
 Only works for market-based parameters – can’t analyze mortality or lapse scenarios
 Fit to insurance liabilities
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Non-existent in actuarial modeling techniques!
Why?
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Availability
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Entire population
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Detailed policy information
Leads to seriatim calculations or grouping methods
Perception that more detail is always better
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Analysis of entire population gives more precise information than analysis of a random sample
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Sampling error difficult to quantify
Lacking a bridge between academia and industry
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UConn Actuarial Center is that bridge towerswatson.com
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Towers Watson Replicated Stratified Sampling (RSS)
Our patent-pending approach rapidly accelerates run times for many actuarial models, and has the following characteristics:
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Based on sound fundamentals of statistical inference
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Combination of stratified sampling and sample replication
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Reduces run time for any complex stochastic model
 with large underlying population
 with easy access to underlying population
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Produces stable results
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Produces robust results with measurable, pre-determined sampling error
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Simple to understand, implement and maintain towerswatson.com
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Does not attempt to “simplify” or “approximate” the underlying population characteristics.
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Builds on the existing company actuarial models.
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Allows for detailed analysis of cash flows under both economic scenarios (equity and interest rate changes) and changes in actuarial assumptions (mortality, lapses, policyholder behavior, etc).
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The entire underlying population distribution is approximated under
RSS at a prescribed level of accuracy for each quantile.
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Convergence time is independent of the size of the population.
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Convergence speed and accuracy of RSS technique are based on wellestablished and tested statistical inference theory.
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RSS technique applied to a variable annuity block of a major life insurance company.
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Analyzed impact of
- an immediate 15% drop in equity funds on VACARVM reserves
- an immediate 3 5% drop in equity funds on VACARVM reserves
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Analysis done for 3 legal entities both before and after reinsurance .
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Analysis compared the change in the VACARVM reserve in the population versus using the RSS technique on 50, 100, 150 and 200 samples of 30 policies each.
A

B
Error rate defined as:
B where A = change in VACARVM reserve using the RSS technique
B = change in VACARVM reserve in the population towerswatson.com
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Legal
Entity
1
2
3
After Reinsurance
Number of policies
Baseline
Reserves
1,027,572 -2,765,845
397,781 -13,298,401
547,883 -3,470,570
Sensitivity 1
Reserves
-4,605,188
-19,171,991
-12,610,502
Sensitivity 2
Reserves
-11,714,900
-20,009,138
-87,276,482
POP
Ratio 1
1.665
1.442
POP
Ratio 2
4.236
1.505
3.634
25.148
Legal
Entity
1
2
3
Number of policies
Before Reinsurance
Baseline
Reserves
Sensitivity 1
Reserves
1,027,572 -79,535,358 -168,055,144
Sensitivity 2
Reserves
-582,368,081
397,781 -890,538,871 -1,621,720,896 -3,807,237,541
547,883 -8,777,155 -27,902,521 -178,654,004
POP
Ratio 1
2.113
1.821
3.179
POP
Ratio 2
7.322
4.275
20.354
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Legal
Entity
1
2
3
After Reinsurance Before Reinsurance
Legal
Entity
# Of samples
50
100
150
200
50
100
150
200
50
100
150
200
RSS
Ratio
POP
Ratio
Error
Rate
1.513
1.665
9.14%
1.615
3.00%
1.640
1.52%
1.667
0.12%
1.611
1.442
11.73%
1.486
1.424
3.10%
1.25%
1.450
0.59%
3.015
3.634
17.02%
3.482
3.735
3.633
4.18%
2.78%
0.02%
1
2
3
# Of samples
50
100
150
200
50
100
150
200
50
100
150
200
1.818
1.822
2.853
3.028
3.153
3.177
RSS
Ratio
2.067
2.124
2.106
2.110
1.826
1.812
POP
Ratio
2.113
1.821
0.17%
0.03%
3.179
10.24%
4.74%
0.82%
0.07%
Error
Rate
2.17%
0.51%
0.32%
0.15%
0.25%
0.49% towerswatson.com
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Legal
Entity
1
2
3
After Reinsurance Before Reinsurance
Legal
Entity
# Of samples
50
100
150
200
50
100
150
200
50
100
150
200
RSS
Ratio
POP
Ratio
Error
Rate
2.771 4.236 34.58%
3.783 10.68%
4.071
4.216
3.88%
0.45%
1.117 1.505 25.75%
1.339 11.00%
1.386
1.506
7.89%
0.10%
17.574 25.148 30.12%
23.239
26.601
25.225
7.59%
5.78%
0.31%
1
2
3
# Of samples
50
100
150
200
50
100
150
200
50
100
150
200
RSS
Ratio
POP
Ratio
Error
Rate
5.575 7.322 23.86%
7.043
7.099
7.330
3.81%
3.04%
0.10%
4.884 4.275 14.24%
5.117 19.70%
4.652
4.282
8.81%
0.15%
13.845 20.354 31.98%
19.059 6.37%
21.203 4.17%
20.336 0.09% towerswatson.com
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Significantly reduces run time, allowing more flexibility and transparency in trade-offs between speed and accuracy:
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Increase accuracy
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Run more stochastic scenarios, improving tail risk analysis
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Reduce use of grouping techniques, improving risk analysis in general
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Reduce use of shortcuts in modeling approach, decreasing model risk
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Map complex investment funds directly, eliminating basis risk
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Minimize sampling bias
Increase speed
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Maintain model and population complexity but decrease run time
Broad Applicability
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Can be used across a range of models and calculations towerswatson.com
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U.S. GAAP
SFAS 133, SOP 03-1
Production, impact testing, forecasting
VACARVM
Production, impact testing, attribution analysis
Economic
Strategic Planning
Capital
Hedge Programs
Hedge effectiveness testing, Explanation of breakage
PBA for life insurance products
Analysis of Inforce
Profitability
Any type of analysis that relies on complex, stochastic calculations is a candidate for the RSS approach towerswatson.com
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RSS is ideally suited for any type of “what if” management analysis
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Instead of 1,000 scenarios, run 10,000 or 100,000
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Instead of 5 or 10 sensitivities, run 50, 100, or 500
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Results are more robust, more accurate, more timely and therefore more actionable
Using RSS, management can be prepared for so called 4 th quadrant (low probability, high severity) events that threaten the long-term sustainability of the insurance industry.
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Mathematical proof, using existing convergence theorems in statistics, that the RSS algorithm generates unbiased and efficient estimates of the change in the population risk measure and is independent of the underlying risk measure being analyzed.
Analytical justification, using numerical analysis and asymptotic techniques, on the number of replications required to achieve a prescribed accuracy level of the RSS estimate of the change in the population risk measure.
Use of clustering analysis techniques to determine the optimal set of risk classes in order to minimize processing time subject to a prescribed level of accuracy of the RSS estimates.
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Complex actuarial modeling in response to increasingly complex insurance products has led to run times that are prohibitive.
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To cope, management has been forced to make trade-offs that are costly either in speed, accuracy or dollar costs.
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Towers Watson’s Replicated Stratified Sampling (RSS) approach offers a paradigm shift in measuring and managing risk using actuarial modeling, by dramatically reducing run time for:
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Stochastic models, including hedging tools,
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Models with large databases,
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Models with easy access to underlying population.
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The RSS approach allows management more flexibility to proactively participate in the risk management process and better understand the impact of current and potential market, economic, actuarial and customer behavior changes.
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Contact details
Jay Vadiveloo, PhD, FSA, MAAA, CFA
Towers Watson Consulting Actuary
Towers Watson Professor, University of Connecticut
Work: (860) 843-7073
Cell: (860) 916-1010
Email: Jay.Vadiveloo@towerswatson.com towerswatson.com
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