Modelling Flashcards
What are the characteristics of a good model?
Must be valid, rigorous enough for its purposes and adequately documented
Model points should reflect risk profile of business being modelled
Parameters must allow for all significant features of business being modelled
Have appropriate input parameters and parameter values
Be communicable and output verifiable
Not be overly complex or time consuming to run
Be capable of development and refinement
Be capable of being implemented in range of ways
Dynamic i.e. parameter need to interact e.g. assets and liabilities
What are uses of models?
FINANCIAL MODELING & VALUATIONS
Model Office
New business model
Existing business model
Full office model
Single policy profit test model
Projections
Embedded values
Takeover valuations
CAPITAL & SOLVENCY
Capital Modeling
Solvency assessments
Capital requirements
Statutory reserves
Management accounting reserves
PRICING & PRODUCT
Pricing Models
New product pricing
Option costing and reserving
Lives and membership projections
Lapse investigations
Sales team support
RISK & INVESTMENT
Asset-Liability Modeling (ALM)
Asset-liability interactions
Investment strategy
Risk assessment
Risk investigations
SCENARIO ANALYSIS
Parameter sensitivity
Scenario analysis
Stress testing
Management actions testing
What is multi-state modelling?
These models are used where members or policyholders can exist in different states, with different associated cashflows and transition probabilities.Assumptions are required for transition intensities between states, which are written as:
μxij = transition intensity at exact age x from state i to state j (i ≠ j).There should be at least the same number of states as there are categories of benefit level
Cashflow vs formula approach (relate to deterministic vs stochastic)
Formula approach is simpler and suitable for ST, less complex products
Cashflow more appropriate where interactions and assumptions vary
Cashflow approach offers more detailed insights and flexibility at cost of complexity
Cashflow approach allows for more robust sensitivity testing
Formula approach doesn’t account for reserves, net negative cashflows and future changes in assumptions but cashflow approach does.
More complex and data-intensive, requiring modelling tools and can be time-consuming.
Deterministic vs stochastic models
Outstanding claim provision
Risk adjustment
Risk monitoring techniques
Requirements of a model
Cash Flow Inclusion: The model must account for all potential cash flows, influenced by the contract structure (e.g., premium and benefit details) and any discretionary benefits, such as options for policyholders.
Supervisory Reserves: The model should accommodate cash flows related to reserves needed for supervisory compliance, including solvency capital that exceeds these reserves.
Types of Cash Flows: It’s important to differentiate between physical cash flows (actual money movements) and notional cash flows (which do not involve physical exchanges).
State Projections: The model needs to project cash flows based on various states of policyholders (e.g., healthy, incapacitated, receiving benefits) and may require subdivisions for different benefit levels.
Dynamic Interaction: The model should ensure consistent interaction between assets and liabilities, reflecting real-world dynamics. This includes adapting the investment strategy based on changing conditions (e.g., worsening solvency).
Stochastic Modeling: It should allow for stochastic modeling to simulate various scenarios and distributions of claims, especially for guaranteed future payments. This involves linking financial and demographic variables dynamically.
Steps in modelling process
- Set out the objective of the process.
- Select an appropriate model structure.
- Decide which variables to include and define inter-relationships.
- Determine the types of scenarios to model.
- Collect data and make adjustments where needed.
- Determine model points.
- Choose suitable density functions for each stochastic variable, if applicable.
- Ascribe values to non-stochastic variables.
- Estimate parameters.
- Construct and run.
- Aggregate output.
- Test and validate reasonableness of results.
- Check and analyse model fit and significance of variables. 14. Perform sensitivity testing.
- Extract and interpret results.
- Document and check the process.
- Summarise results and draw conclusions.
Formula approach definition
Overview: Calculates premiums or contributions by equating forecast income (premiums/contributions) with forecast outgo (claims, expenses, commissions, etc.).
Focuses on short-term balance between income and outgo, with assumptions on inflation and interest rates.
Ignores reserves, net negative cashflows, and future changes in assumptions; does not measure sensitivity to changes in experience.
Use Case: Suitable for simpler, short-term insurance products or defined benefit pension funds where straightforward projection of premium or contribution rates is needed.
Cashflow approach
Projects detailed future cashflows (e.g., premiums, claims, expenses) for individual model points or cohorts, allowing for more complex interactions and assumptions.
Handles long-term projections and complex product features, accounting for reserves, capital requirements, and reinsurance.
Use Case: Best for long-term insurance or pension fund assessments where a more detailed projection of profitability, reserves, or funding status is needed.
Challenges: More complex and data-intensive, requiring modelling tools and can be time-consuming.
Disadvantages of the formula approach
Allowing for the proper timing of events
Allowing for the accumulation of reserves (reserves are ignored completely when using this approach).
Allowing for capital needs
Allowing for the impact of net negative cashflows in any period
Allowing for separate inspection of premium-related cashflows or claim-related cashflows, that is tracking expenses, claims, premiums, etc. separately each year
Allowing easily for variation of assumptions over time
Allowing for changes in the assumed future experience and cannot be used to measure the sensitivity of profit to such variations
Allowing for more complicated product or benefit structures.
Risk Neutral vs. Real-World Calibration
Risk-Neutral Calibration (or market-consistent): Used for valuation purposes, particularly for options and guarantees. It replicates the market prices of financial instruments and adjusts probabilities to match market observations.
Real-World Calibration: Used for projecting future scenarios and calculating capital. It uses realistic assumptions about future events and real-world probabilities. For example, equities might be expected to outperform bonds due to higher risk.
Cashflow approach: Cohort approach vs. model point approach
Model point approach: each policy is represented using a MP, and premium calculated for each MP.
Results in greater accuracy because model captures unique features of each policy.
But time-consuming and computationally expensive if large amount of policies.
Cohort approach: policies are groups in cohorts e.g. age (40-45) or policy term (10-15 years).
For each cohort, average assumptions applied to represent group.
Cross-subsidisation will occur within the group, so be careful of policy mix.
Approach used for large portfolios, as is reduced complexity.
Multiple linear regression to GLM
