1. Financial Risk Management of Insurance Enterprises
Dynamic Financial Analysis
1. D’Arcy, Gorvett, Herbers, and Hettinger - Contingencies
2. D’Arcy and Gorvett - JRI 1

2. Overview
What is DFA?
How is it different from other modeling procedures?
How did DFA evolve?
What are the basic approaches in DFA modeling? 2

3. Dynamic, Financial, Analysis
“Energy, continuous activity, intensity, interactive”
Insurer variables are not fixed, but stochastic
Financial
“Related to management of money or investments”
Evaluate insurer activities, both liabilities and assets
Analysis
“Examination of an interrelated system and its elements” 3

4. Definition of Dynamic Financial Analysis (DFA)
Casualty Actuarial Society definition:
Analyze the financial condition of an insurance enterprise
Financial condition refers to ability of capital and surplus to meet future obligations of insurer in “unknown future environment”
For life insurers, similar modeling procedures are known as dynamic solvency testing or dynamic financial condition analysis 4

5. A Broader Concept DFA does not need to focus only on solvency issues
Other uses:
Model ongoing operations over time instead of concentrating on the current position
Determining the sensitivity of financial results to various environmental factors
Identify specific scenarios where the insurer is exposed to significant risk of loss
Valuation of a line of business or entire insurer 5

6. Definitions Appointed actuary
A “qualified” actuary that is appointed by the Board of Directors of an insurer
Files actuarial opinion with the states stating that all reserves are appropriate and assets are adequate to meet liabilities 6

7. Analytic vs. Simulation
Analytic model provides exact solution based on precise relationships
Simulation models can be used if exact mathematical representations do not exist
Can accommodate complex relationships
The “answer” in a simulation model is not just one number
It is a range or distribution of plausible results 7

8. Prior Techniques
Previous models evaluated insurer strategies under certain assumptions with respect to:
Asset returns
Underwriting results
Economic environment (recession, expansion)
Typically, these models ignored interaction of assets and liabilities
The future was assumed to be essentially the same as the present
Regardless of lifetime of policy/project 8

9. The Impetus Behind DFA Interest rate fluctuations in the 1970s
Life insurers are sensitive to interest rate changes
Disintermediation resulted from high interest rates
Rating agencies began to consider effect of interest rate swings on surplus/solvency 9

10. The “Seeds” of DFA
RBC is first attempt at linking capital to risk of insurers
The various RBC factors are the same for all insurers
RBC has short term focus
DFA customizes the analysis by accounting for specific insurer business plan both now and in the future 10

11. The DFA Approach Model variability of all important variables
Claims, catastrophes
Asset returns
Premium income
Account for correlation among all factors within each scenario
When modeling the entire insurer, include correlation among lines of business
Project cash flows under the assumptions
Determine the insurer’s financial position 11

12. Two Approaches to DFA: (1) Scenario Testing
Select several assumptions for all variables
e.g., optimistic, pessimistic, and average
A scenario is a set of assumptions about the future environment
Determine financial position
Better than point estimate but does not provide any likelihood information
Range of outcomes is frequently too wide to make decisions 12

13. Two Approaches to DFA: (2) Stochastic Simulation
Select distributions for and correlations among all variables
Draw randomly from each distribution
Determine the aggregate financial outcome for each iteration
Incorporate any variable interactions
Analyze distribution of outcomes 13

14. Uses of Stochastic Simulation
Stochastic simulation provides more information than scenario testing
Use of information depends on objectives
How often does insurer go insolvent?
Which assumptions are the most critical?
What accounts for good/bad scenarios?
If possible, select hedges to protect against bad scenarios 14

15. Categories of Insurer Risk
Balance sheet risk
Changes in value of assets and liabilities
Operating risk
Investment and underwriting activities
Actuaries have traditionally looked at liabilities and underwriting
Balance sheet and operating risks are interrelated 15

16. Building a DFA Model Determine the objective
Evaluating solvency, valuation of a block of business or insurer
Include only the most relevant factors
Only model general asset classes such as bonds, equities, and mortgages
Reserves should reflect economic value and incorporate discounting
Model only the factors that are measurable 16

17. Variables in a DFA Model
Claim distributions are a result of frequency and severity
Frequency of claims is affected by:
Catastrophe
Society trends (e.g., smoking, speed limit)
Severity of claims is affected by inflation 17

18. DFA for Life Insurers
Life insurer products are long term and are interest rate sensitive
Option of policyholder to withdraw is very important
Cash flow testing is a primitive form of DFA
Test adequacy of assets vs. liabilities under a few scenarios
NY Regulation 126 specifies seven scenarios 18

19. NY 126 Interest Rate Scenarios
Remain level for 10 years
Increase ½ % per year for 10 years
Increase 1% for 5 years, then decrease 1% for 5 years
Pop-up 3% immediately, then level
Pop-down 3% immediately, then level
Decrease ½ % per year for 10 years
Decrease 1% for 5 years, then increase 1% for 5 years 19

20. Dynamic Financial Analysis Model
How to Access and Run DFA Model
Components of Model
Underwriting Module Catastrophe Module
Financial Module Tax Module
Reinsurance Module
Generating and Using the Output
Future of DFA

21. Basics of DFA Model Model will be available for general use at:
Runs with Microsoft Excel
Entire model to be subject to peer review
Key variables of concern to U.S. property-liability insurers will be included
Model will be as simplified as practical
Flexibility for future enhancements
Potential use as a DFA teaching tool

22. Underwriting Module Loss Frequency and Severity Rates and Exposures
Underwriting Cycle
Jurisdictional Risk
Aging Phenomenon

23. Catastrophe Module Number based on Poisson distribution
Focal point determined
Size based on lognormal distribution
Geographical distribution determined by correlation matrix
Loss allocated to company based on market share

24. Financial Module Financial Variables Short-Term Interest Rate
Term Structure
Default Premium
Default Risk
Equity Premium (Market Risk Premium)
Inflation

25. Short-Term Interest Rate
Based on U.S. Treasury Bill rate
Considered the “Workhorse” Variable
Correlated with other variables
Impacts market values of assets
Add risk-premiums to derive other asset rates of return
Term premium
Default premium
Equity premium

26. Short-Term Interest Rate
Cox-Ingersoll-Ross Model
dr = a(b-r)dt + sr0.5dz
r = short term interest rate
a = speed of mean reversion =
b = mean interest rate =
s = volatility parameter =
Volatility proportional to square root of r
Values taken from Chan, et al, 1992 Journal of Finance

27. Inflation Affects future values of liabilities Function of:
Contemporaneous interest rates
Current yield spreads
Some autoregressive properties
Three-step simulation process
Simulate short-term interest rate
Simulate general inflation rate
Determine claim inflation by line of business

28. Tax Module
Calculates income taxes based on both standard corporate tax rate and alternative minimum tax

29. Reinsurance Module Current approach Quota share reinsurance
Under development
Excess of loss
Catastrophe
Aggregate excess

30. Using the DFA Output Proportion of outcomes that are unacceptable
Revise operations and rerun
Analysis of the unacceptable outcomes
Reduce risk that led to result
Useful for:
Solvency Testing
Business Planning

31. The Future of DFA Is becoming a widely used actuarial tool
Will cause actuaries to work on both asset and liability sides of insurance business
Will require actuaries to become proficient with financial tools and techniques
Will increase the importance of finance on actuarial exams

32. Reminder!!! Exam 2 is Tuesday, April 10
Exam is 1-2:20 pm in 429 Armory
Open book, open note 19

33. Exam 2 Calculations and explanations Focus is on lectures 13-20
ALM
Duration and convexity
Stochastic processes
Interest rate models
Binomial method and simulation
Interest rate options
CMOs
Valuing swaps
Understand material prior to first exam
Derivatives
Need for financial risk management

34. Pre-Exam Office Hours
Monday, April 9
1-3 pm
311 Wohlers Hall