Chapter 27

Question 1

How are option prices used to determine the cost of an investment guarantee in life insurance policies?

Answer 1

• Analogies:
  
  • GMMV (Guaranteed Minimum Maturity Value): European put option; exercise price = maturity guarantee; insurer “writes” the put.
  • GMSV (Guaranteed Minimum Surrender Value): American-style put; policyholder can surrender early; insurer grants early-exercise option.
  • GAR (Guaranteed Annuity Rate): Call option on bonds or swaption (floating → fixed rate) to meet guaranteed annuity.
  • Cost Determination:
  • Market price of similar financial derivatives ≈ expected present value of the guarantee.
  • Extra premium estimated via the market cost of acquiring equivalent options.
  • Market Considerations:
  • Guarantees often initially out-of-the-money → no intrinsic value, only time value.
  • Time value reflects potential future cost if adverse market movements occur.
  • Practical Notes:
  • Exact replication via traded options is rare; approximations use market indices.
  • Market-based valuation does not require the insurer to purchase derivatives; hedging is separate.

Question 2

How is stochastic simulation used to determine the cost of investment guarantees in insurance contracts?

Answer 2

• Purpose: Estimate extra funds needed to meet guarantees (e.g., unit-linked or non-linked policies) under uncertain investment returns.
  
  • Core Principle: Simulate many possible future asset scenarios; the average cost of meeting the guarantee = expected cost.
  • Calculation Steps:
    1. Model stochastic investment returns (mean, variance, distribution).
    2. Run multiple simulations (e.g., 10,000) over the policy term.
    3. Project policy fund for each run (premiums minus charges).
    4. Determine cost if fund < guaranteed value.
    5. Average costs across all runs → expected guarantee cost.
    6. Discount costs to present value to get liability estimate.
  • Key Assumptions:
  • Policyholder behavior (e.g., take-up rates of options).
  • Market-dependent liabilities (e.g., GAR) consistent with asset simulations.
  • With-profits policies → future bonus declarations modeled consistently.
  • Result: Provides an estimate, not an exact value; final premiums = expected cost + margin.
  • Advantage: Captures range of possible outcomes and tail risk, unlike deterministic methods.

Question 3

What is the difference between stochastic simulation and option-pricing techniques for costing insurance guarantees?

Answer 3

• Option Pricing:
  
  • Uses market prices of corresponding financial derivatives.
  • Provides a market-based estimate of guarantee cost.
  • Relies on traded options or swaps that mimic the guarantee.
  • Stochastic Simulation:
  • Models a range of possible investment scenarios to project fund outcomes.
  • Calculates expected additional costs needed to meet the guarantee.
  • Provides an estimate, not an exact value (subject to simulation error and model assumptions).
  • Key Difference:
  • Option pricing = market-based; stochastic simulation = scenario-based estimate.

Question 4

How is the cost of simple mortality options assessed in insurance?

Answer 4

• Definition:
  
  • Mortality options let policyholders extend term or increase cover at standard rates without medical evidence.
  • Cost arises from anti-selection: higher-risk lives exercising the option.
  • Cost = premium that should have been charged (full underwriting) − premium actually charged.
  • Main Factors Affecting Cost:
    1. Health status of those exercising the option.
    2. Proportion of lives who exercise the option (take-up rate).
  • Valuation Method:
  • Use cashflow projections including:
  • Additional benefits payable under the option.
  • Additional premiums expected to be received.
  • Extra administrative expenses.
  • Include reserves if purpose is pricing, not just liability.
  • Key Assumptions:
  • Probability of Exercise: Take-up rates, realistic or simplified.
  • Benefit Level: Expected additional benefit chosen.
  • Mortality / Anti-Selection:
  • Mortality heavier for those exercising the option.
  • Modeled via higher % of base mortality or age loading.
  • Ensure overall mortality remains consistent.
  • Expenses: Additional costs of administering the option.

Question 5

What are the main types of options found in insurance contracts and their characteristics?

Answer 5

• Investment Guarantees:
  
  • GMMV (Guaranteed Minimum Maturity Value): European put option; protects against downside at maturity.
  • GMSV (Guaranteed Minimum Surrender Value): American put option; exercised anytime before maturity.
  • GAO (Guaranteed Annuity Option): Call option on bonds or swaption; allows conversion to annuity at guaranteed terms.
  • Found in traditional, unit-linked, and with-profits contracts.
  • Mortality Options:
  • Purchasing Additional Benefits: Extra cover at normal rates without new medical evidence.
  • Renewing the Policy: Extend term insurance without further underwriting.
  • Changing Contract Type: Convert sum assured between contract types (e.g., term → endowment).
  • Cost: Due to anti-selection; difference between fully underwritten premium and standard premium.