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Homework 5 — VM-22 Framework Understanding and Structural Modeling

This assignment is tied to Class 5 (VM-22 Framework and Asset–Liability Reserve Methodology).

The goal of this homework is conceptual mastery, not numerical sophistication.

You should demonstrate that you understand:

  • what VM-22 is designed to do
  • how deterministic and stochastic reserves are constructed
  • how assumptions are classified and governed
  • how VM-22 differs from CARVM and cash flow testing
  • how the overall VM-22 calculation framework is structured

Problem 1 — What Problem Does VM-22 Solve? (Conceptual)

Answer in words.

  1. What regulatory or economic problem is VM-22 designed to address?
  2. Why is a purely deterministic reserve framework (such as CARVM) insufficient for many modern annuity products?
  3. In one sentence, explain the key difference between:
  4. “worst-case benefit” reserving
  5. “asset–liability cash flow” reserving

Problem 2 — Deterministic Reserve Logic (Conceptual)

Answer in words. No calculations are required.

  1. What is the purpose of the deterministic reserve in VM-22?
  2. Why is the deterministic reserve not known in advance and must be solved iteratively?
  3. Define surplus in the context of VM-22 deterministic projections.
  4. What condition must be satisfied at time 0 for the deterministic reserve to be considered sufficient?

Problem 3 — PV Surplus vs Interim Surplus (Conceptual)

Answer in words.

  1. In VM-22, is the binding condition based on:
  2. surplus being positive in every projection year, or
  3. the present value of surplus?
  4. Can interim (year-by-year) surplus be negative in VM-22 projections?
  5. Why might regulators or auditors still care about interim surplus patterns, even if they are not binding?

Problem 4 — Assumptions in VM-22 (Conceptual)

VM-22 uses a mix of prescribed and company-specific assumptions.

4.1 Liability Assumptions

For each of the following, state whether it is typically: - prescribed by regulation, or - company-specific (with margins)

Assumption Prescribed or Company-Specific?
Mortality
Lapse / Withdrawal
Annuitization Election
Expenses
Premiums

4.2 Asset Assumptions

For each item below, briefly explain how it is governed under VM-22.

Assumption Description
Initial Asset Portfolio
Reinvestment Strategy
Reinvestment Yield
Default Rates

Problem 5 — Deterministic vs Stochastic Reserve (Conceptual)

Answer in words.

  1. What additional risk does the stochastic reserve capture that the deterministic reserve does not?
  2. What is a CTE (Conditional Tail Expectation) measure, in general terms?
  3. Why does VM-22 require taking the maximum of deterministic and stochastic reserves?

Problem 6 — VM-22 vs CARVM vs Cash Flow Testing (Conceptual)

Complete the table below.

Aspect CARVM VM-22 Cash Flow Testing
Primary objective
Treatment of assets
Treatment of behavior
Tail risk
Interim liquidity focus

Then answer:

  • In one paragraph, explain how VM-22 can be viewed as a bridge between CARVM and cash flow testing.

Problem 7 — VM-22 Structural Flowchart (Required)

This problem tests your understanding of the overall VM-22 calculation architecture.

You may complete this problem using either Mermaid or Python visualization tools.

7.1 Objective

Create a flowchart that clearly shows:

  • how VM-22 reserves are calculated
  • how deterministic and stochastic components fit together
  • where assumptions and scenarios enter the process
  • how the final reserve is determined

The emphasis is on structure and logic, not artistic detail.

7.2 Required Elements

Your flowchart should include at least the following components:

  1. Assumption setup
  2. liability assumptions
  3. asset assumptions
  4. Deterministic projection
  5. asset cash flows
  6. liability cash flows
  7. surplus calculation
  8. iterative solving for initial reserve
  9. Stochastic projection
  10. multiple economic scenarios
  11. scenario-specific reserves
  12. CTE aggregation
  13. Final reserve determination
  14. comparison of deterministic vs stochastic reserves

7.3 Option A — Mermaid Flowchart

If you choose Mermaid, include a diagram similar in spirit to:

flowchart TD
    A[Set VM-22 Assumptions] --> B[Deterministic Scenario Projection]
    B --> C[Project Assets]
    B --> D[Project Liabilities]
    C --> E[Compute Surplus]
    D --> E
    E --> F[Discount Surplus]
    F --> G{PV Surplus ≈ 0?}
    G -- No --> H[Adjust Initial Assets]
    H --> B
    G -- Yes --> I[Deterministic Reserve]

    A --> J[Stochastic Scenarios]
    J --> K[Scenario Projections]
    K --> L[Scenario Reserves]
    L --> M[CTE Calculation]

    I --> N[Compare Reserves]
    M --> N
    N --> O[VM-22 Reserve]

You may modify, expand, or reorganize this diagram as long as the logic is correct.

7.4 Option B — Python Visualization (Optional)

Alternatively, you may use Python packages such as:

  • graphviz
  • networkx
  • matplotlib (diagrammatic representation)

In this case:

  • include your Python code
  • briefly explain how each part of the diagram maps to VM-22 concepts
# Example (structure only)
from graphviz import Digraph

dot = Digraph()
dot.node("A", "Assumption Setup")
dot.node("B", "Deterministic Projection")
dot.node("C", "Stochastic Projection")
dot.node("D", "Final Reserve")

dot.edges([("A","B"), ("A","C"), ("B","D"), ("C","D")])

Deliverables

Submit:

  1. Written answers for Problems 1–6
  2. A VM-22 flowchart (Mermaid or Python)
  3. A short explanation (6–10 sentences) describing your flowchart and how it represents VM-22 logic

What this homework demonstrates

  • You understand the purpose and structure of VM-22
  • You can distinguish deterministic and stochastic reserves
  • You can explain how assumptions are governed
  • You can clearly communicate VM-22 architecture using diagrams