Overview (Start Here)

1. Scope of the Illustration Tool¶

This project builds a deterministic policy-level illustration engine for a Multi-Year Guaranteed Annuity (MYGA).

The purpose is to understand: - how MYGA product features interact, - how calculation order affects outcomes, - how illustration logic mirrors real insurer systems.

Product Scope¶

Feature	Included
Product Type	MYGA (fixed deferred annuity)
Crediting Rates	Initial guaranteed + renewal rates
Partial Withdrawals	Free withdrawal provision
Surrender Charges	Declining schedule
Market Value Adjustment (MVA)	Yes
Guaranteed Fund	Statutory nonforfeiture floor
Cash Surrender Value	Yes

Modeling Scope¶

deterministic (no scenarios)
single policy
no behavior optimization
annual time step (BOY / EOY)

2. Product Feature Definitions (Concise)¶

This section defines what is modeled, not implementation details.

2.1 Account Value (AV)¶

The Account Value represents accumulated premium and credited interest, net of withdrawals and penalties.

\[ AV_{EOY} = (AV_{BOY} - W_t - \text{Penalty}_t) \times (1 + r_t) \]

Component	Description
\( AV_{BOY} \)	Account value at beginning of year
\( W_t \)	Withdrawal taken
\( r_t \)	Crediting rate for year

2.2 Crediting Rates¶

Period	Rate Type
Guarantee Period	Fixed, declared rate
Post-Guarantee	Renewal rates (year-specific)

Rate selection depends on policy year and guarantee term.

2.3 Partial Withdrawal Provision¶

The contract defines a free withdrawal limit, while the policyholder determines the actual withdrawal taken.

Free Withdrawal Limit¶

\[ \text{FreeLimit}_t = w \times AV_{BOY,t} \]

Rule	Assumption
Timing	Beginning of policy year
Year 1	No withdrawals allowed
Excess	Allowed, but penalized

Withdrawal Constraints¶

\[ W_t = \begin{cases} 0, & t = 1 \\ \min(\text{UserInput}_t,\ AV_{BOY,t}), & t \ge 2 \end{cases} \]

Portion	Treatment
Free portion	No penalty
Excess portion	Subject to surrender charge and MVA

2.4 Surrender Charges¶

Surrender charges apply to amounts treated as surrender behavior.

\[ \text{SC}_t = s_t \times W^{\text{excess}}_t \]

Characteristic	Description
Basis	Excess withdrawal
Pattern	Declining schedule
End State	Typically 0%

2.5 Market Value Adjustment (MVA)¶

The Market Value Adjustment aligns liability payouts with asset market values when withdrawals occur early.

Economic Interpretation¶

Rate Movement	Asset Value	MVA
Rates ↑	Values ↓	Negative
Rates ↓	Values ↑	Positive

MVA Factor¶

\[ \text{MVAFactor}_t = \frac{(1 + x)^n}{(1 + y_t)^n} - 1 \]

Symbol	Meaning
\( x \)	Issue reference rate
\( y_t \)	Current reference rate
\( n \)	Remaining guarantee duration

Application Base¶

Scenario	Amount Subject to MVA
Partial withdrawal	Excess portion after surrender charge
Full surrender	Entire surrenderable amount

\[ \text{MVA}_t = \text{MVA Base}_t \times \text{MVAFactor}_t \]

2.6 Guaranteed Fund¶

The Guaranteed Fund provides a statutory nonforfeiture floor.

\[ GF_t = \alpha P (1 + i_{min})^t - \text{Withdrawals} \]

Parameter	Meaning
\( \alpha \)	Guaranteed percentage (e.g., 87.5%)
\( i_{min} \)	Minimum guaranteed rate

2.7 Cash Surrender Value¶

\[ CSV_t = \max(GF_t,\ AV_t - SC_t + \text{MVA}_t) \]

Ensures compliance with statutory minimums.

3. Calculation Order (Key Principle)¶

Illustration results depend on calculation order.

Core dependencies:

Step	Depends On
Withdrawals	BOY account value
Penalties	Excess withdrawal
MVA	Remaining duration, rates
Interest	Post-withdrawal balance
CSV	AV, SC, MVA, GF

4. Illustration Calculation Flow¶

flowchart TD
    A[Initialize Inputs] --> B[Set Projection Horizon]
    B --> C[Select Crediting Rate]
    C --> D[Compute MVA Factor]
    D --> E[Apply Withdrawal at BOY]
    E --> F[Update Guaranteed Fund]
    F --> G[Credit Interest]
    G --> H[Apply Surrender Charge]
    H --> I[Apply MVA]
    I --> J[Compute CSV]
    J --> C