Chapter 11 Notes: Pricing and Valuation in Life Insurance

1. Informational: Core Concepts of Insurance Pricing & Premium Structure

Premium Definition & Types

The premium is the price paid by an insured to purchase an insurance policy, typically expressed as a rate per thousand rupees of sum assured. Premium rates published in company tables are known as Office Premiums or Tabular Premiums, which represent level annual payments remaining constant throughout the policy term.

• Single Premium: A one-time lump-sum payment at contract inception, primarily investment-oriented.
• Regular Premium: Level annual, half-yearly, quarterly, or monthly payments made over the premium-paying term.

Premium Rebates & Extra Charges

Insurers offer premium discounts (rebates) or impose extra charges based on policy size, payment frequency, and risk profile:

• Rebate for Sum Assured: Offered on higher sum assured policies because administrative servicing costs remain fixed regardless of policy size, allowing operational savings to be passed to the buyer.
• Rebate for Mode of Premium: Annual and half-yearly payment modes save administrative processing frequency and allow insurers to earn investment interest upfront. Monthly modes incur higher administrative expenses and may attract extra charges.
• Standard vs. Sub-Standard Lives:
  • Standard Lives: Individuals with average mortality risk who are charged standard tabular rates.
  • Sub-Standard Lives: Individuals with physical impairments (e.g., diabetes, heart conditions) or hazardous occupations (e.g., circus acrobat) who are charged extra premiums (health extra or occupational extra).
  • Rider Extras: Supplementary covers such as Double Accident Benefit (DAB) or Permanent Disability Benefit (PDB) are funded via specific extra premium loadings.

Single-Line Pricing Formulas

• Net Premium = Present Value of Expected Future Claims
• Gross Premium = Net Premium + Expense Loading + Contingency Loading + Bonus Loading

2. Commercial Investigation: Actuarial Valuation, New Business Strain & Risk Factors

Actuarial Determination of Premium

Actuaries set premium rates using two primary foundational elements:

1. Mortality: Expected death rate at a given age derived from a Mortality Table. Higher mortality leads to higher premium rates.
2. Interest Rate: Discount rate used to calculate the present value of future claim liabilities. Higher assumed interest rates lead to lower premiums.

Guiding Principles for Premium Loading

Gross premiums add "loading" to net premiums based on three core principles:

1. Adequacy: Total loading must cover all operating costs, safety margins, and contribute to company surplus.
2. Equity: Operating expenses must be equitably apportioned among policy classes so one class does not subsidize another.
3. Competitiveness: Resulting gross premiums must remain competitive in the market.

New Business Strain & Gestation Period

In the first policy year, initial acquisition expenses (agent commissions, medical examiner fees, stamp duty, setup overheads) plus required statutory reserve margins exceed the initial premium collected. This initial financial deficit is called New Business Strain. It is recouped from subsequent renewal premiums, creating a gestation period of several years before a life insurance company turns profitable.

Policy Lapses vs. Withdrawals

• Lapse: Discontinuation of premium payments by the policyholder (highest occurrence occurs in the first policy year).
• Withdrawal (Surrender): Voluntarily terminating a policy in exchange for its acquired cash/surrender value.

Valuation of Assets and Liabilities

Periodical valuation evaluates insurer solvency and determines available surplus:

• Surplus = Value of Assets - Value of Liabilities
• Asset Valuation Methods:
  1. Book Value: Acquisition/purchase cost of the asset.
  2. Market Value: Current market price of the asset.
  3. Discounted Present Value: Discounted future income stream from the asset.
• Conservative vs. Liberal Valuation: Conservative valuation overstates liabilities and understates assets, reducing declared surplus today but strengthening long-term financial soundness for future policyholders.

3. Transactional: Surplus Allocation, Bonus Mechanisms & ULIP Pricing

Surplus Allocation

Once valuation generates a surplus, it is allocated across three streams:

1. Solvency Margin: Statutory cushion set aside to absorb unforeseen adverse deviations.
2. Free Assets: Unencumbered surplus retained to fund business expansion.
3. Divisible Surplus: Distributed as bonuses to participating ("With Profit") policyholders and shareholders.

Reversionary Bonus Types

• Simple Reversionary Bonus: Declared as a flat amount per thousand sum assured.
• Compound Bonus: Declared as a percentage applied to the basic sum assured plus already attached bonuses.
  • Single-Line Formula: Compound Bonus = % of (Basic Sum Assured + Attached Bonuses)
• Super Compound Bonus: Applies separate percentages to the basic sum assured and attached bonuses.
• Terminal Bonus: Non-guaranteed windfall bonus declared upon contractual termination (death or maturity) after long policy durations.

Contribution Method (North American Model)

Distributes surplus directly based on three sources: mortality savings, interest gains, and expense savings. Payouts occur via cash dividends, premium reductions, paid-up additions, or interest-bearing accumulations.

Unit Linked Insurance Plan (ULIP) Pricing

ULIPs feature an unbundled, transparent structure:

• ULIP Premium = Policy Allocation Charge + Mortality Charge + Investment Component
• Policy Allocation Charge (PAC): Covers initial setup, administration, and agent commissions.
• Unit Allocation: Balance premium purchases investment units valued at Net Asset Value.
  • Single-Line Formula: Net Asset Value = Total Market Value of Fund Investments / Total Number of Units
• Risk Bearing: The investment risk is borne entirely by the insured/policyholder, while the insurer bears mortality and expense risks.

4. Exam Key Takeaways & Quick Reference

• Primary Pricing Elements: Mortality, Interest, Expenses, Reserves, Bonus Loading (Rebate is NOT a factor in determining premium).
• Interest vs. Premium Relationship: Higher interest rate assumed = Lower premium.
• Book Value: Original purchase/acquisition cost of an asset.
• New Business Strain Cause: Excess initial acquisition expenses and reserve requirements at the proposal stage.
• ULIP Investment Risk: Borne completely by the policyholder.
• Minimum Policy Tenure for Guaranteed Surrender Value: 3 consecutive years of paid premiums.