11.1 Modelling

Question 1

What are the approaches available to produce solutions to actuarial or financial problems?

Answer 1

New Model: Developed in-house.
Modification: Of an existing model.
Commercial Product: Purchased externally.

Question 2

What are the factors to consider when deciding the type of model to solve a problem?

Answer 2

Decision factors include:
* Desired accuracy
* Available expertise
* frequency of use
* flexibility
* cost
* data appropriateness
* fit for purpose
* uniqueness

Question 3

What are the types of models used in actuarial and financial modelling?

Answer 3

Deterministic Models: Use predefined rules and equations for predictions; common in financial projections and valuations.

Stochastic Models: Incorporate randomness and uncertainty; Monte Carlo simulations assess risk and uncertainty.

Question 4

List ten areas of a life insurance company’s activities that might require an actuarial model

Answer 4

1. Financial projections
2. Budgeting and financial planning
3. Calculating provisions for claims
4. Proving solvency to the regulator
5. Pricing new/existing products
6. Setting actuarial assumptions
7. Calculating capital requirements
8. Business strategy
9. Valuing guarantees/options
10. Assessing reinsurance requirements

Question 5

What operational issues should be considered in designing and running actuarial models?

Answer 5

Purpose: Fit for solving a problem.
Data: Accuracy, relevance, completeness, consistency.
Assumptions: Demographic, economic, behavioural.
Model Design: Flexibility, simplicity, transparency.
Validation: Internal and external validation, sensitivity and scenario analysis.
Efficiency: Computational resources, automation, scalability.
Governance: Documentation, audit trail, compliance.

Question 6

Sources of data

Answer 6

Internal Data: Historical experience from the company’s own past business (e.g., claims, policyholder demographics, lapses).

Industry Data: Pooled data from multiple insurers, industry-wide mortality/morbidity tables, and statistics from professional bodies.

Population Data: National statistics from government agencies (e.g., census data, national mortality and health statistics).

Reinsurer & Consultant Data: Expertise, proprietary data, and pricing insights from reinsurers or specialized data consultants.

Expert Research: Academic studies, medical papers, and economic forecasts that inform future trends and assumptions.

Question 7

How are models used for pricing insurance contracts?

Answer 7

• Uses deterministic discounted cash flow models.
• Set profit targets,
• Gather historical data,
• Divide data into homogenous groups
• Set assumptions.
• Project and discount cashflows,
• Adjust premiums until profit targets are satified.
• Consider marketability and competitiveness, monitor assumptions

Question 7

General Data Issues

Answer 7

Relevance: The data may not be representative of the specific product, demographic, or time period being priced.

Credibility: The volume of data may be too small to be statistically reliable.

Accuracy & Consistency: The data may contain errors, missing entries, or inconsistencies in how it was recorded over time.

Availability: The desired data may not exist, especially for new products or markets.

Future Projections: Historical data is not a perfect predictor of the future; it requires actuarial judgment to adjust for expected trends and changes (e.g., medical advances, inflation, climate change).

Credibility vs. Relevance: The need to balance using a large, credible dataset against using a smaller, more relevant one.

Question 8

Describe the process of valuing liabilities using actuarial models

Answer 8

• Use deterministic discounted cashflow models.
• Gather data, set assumptions and project cashflows.
• Accounting for decrements, discount net cashflows.
• Add buffers for extreme scenarios
• Ensure regulatory compliance of provisions.
• Document methodology and assumptions

Question 9

How are actuarial models used for valuing options and guarantees?

Answer 9

• 1. Use a stochastic model
• 1. Set assumptions, specify correlations, gather data.
• 1. Run a large number of scenarios
• 1. Project cashflows of the cost of the guarantee for each scenario,
• 1. Discount the cashflows using an appropriate discount rate
• 1. Rank them from favourable to worse and assess the variability of results e.g. quartiles, 5th and 95% percentile
• 1. Choose probability of ruin, e.g. 1 in 1000 -> 99.99% percentile
• 1. Regularly monitor and update the provision for changes in economic conditions and experience.

Question 10

How are models used to set future financing strategies for benefit schemes?

Answer 10

Data Collection:

• Categorise existing membership (e.g., actives, deferred, current pensioners) using model points.
• Represent potential new members with model points at average entry age and salary.

Modelling Expected Cashflows:

• Determine financing strategy based on amount and timing of future contributions.
• Model cashflows from existing assets and future contributions, accounting for decrements (death, withdrawal, transfer out, ill-health, retirement).

Deficit Management:

• Unlike insurance companies, benefit schemes can show a deficit if the sponsor (employer) can cover the shortfall over an acceptable time period.

Question 11

How does sensitivity analysis aid in decision making?

Answer 11

Involves re-running models with different parameters to illustrate potential deviations. Helps to:
* Illustrate the likely range of actual experience.
* Create a probability distribution for potential outcomes.

Benefits:
* Identify significant parameters,
* assess risks,
* inform decisions,
* support scenario planning.