C30 CIA DISCOUNT

Discount Rate

Rate used to discount estimate of future CFs

• Consistent w/ timing, liquidity, currency of insurance contract CFs

• Can be a single rate → spot rate

  • Or curve of rates varying by duration → yield curve

Fulfilment Cash Flows (FCF)

PV of ests of future CFs + RA for non-financial risk

Liquidity/Illiquidity Premium

Adjustments to liquid risk-free yield curve

• Reflects diff in liquidity characteristics between financial instruments underlying risk-free rates & insurance contracts

Liquidity prem → insurer invests in gov bonds

Low risk & easily converted to cash

• Liquidity prem = 0

Liquidity prem → insurer invests in biotech startups

High risk & difficult to convert to cash

• Liquidity prem high

Reference Portfolio

Portfolio of assets used to derive discount rates based on current market rates

• Adj to remove risk char NOT in insurance contracts

Factors that may differ between reference portfolio vs insurance contracts

• Liquidity

• Currency

• Timing

• Investment risk

  • Credit risk

  • Market risk

How to address diff in timing risk?

Assess consistency of timing of payments between reference portfolio vs insurance contracts

How to assess currency risk?

Select reference portfolio made up of investments in same currency as insurance contracts

Estimating FCFs → Grouping wrt Reinsurance

• Estimate net

  • Net = Gross - Ceded

    • = (Direct + Assumed) - Ceded

• Estimate gross & ceded separately

  • Gross = Direct + Assumed

  • Ceded

Net vs Gross/Ceded of Reinsurance → Considerations

DV-Re

• Data availability

  • If sparse, hard to directly estimate PV of ceded CFs

• CF Volatility

  • Diff segments of business may use diff groupings depending on volatility of CFs

• Reinsurance Held

  • Consider type & consistency of reinsurance held

Segmenting data for payment patterns → Considerations

• Business segments used for analyzing undiscounted liabilities

• Payout period

• Existence of predetermined payment schedule

Discount Rates → Characteristics

• Reflect TVM, liquidity, & char of CFs of insurance contracts

• Consistent w/ market prices for financial instruments w/ similar CF characteristics as insurance contracts

• Exclude factors that don’t affect CFs in insurance contracts

Discount Rate → Bottom-up Method

Liquid, risk-free yield curve

• Adj to reflect diff in liquidity char between financial instruments underlying risk-free rate vs insurance contracts

Discount Rate = Risk-free Rate + Liquidity Prem

Discount Rate → Top-down Method

Yield to maturity of reference portfolio

• Remove factors not relevant to insurance contracts

  • Ex: credit & market risk

Discount Rate = Ref Portfolio Rate - Credit/Market Risks & Other Adj

Advantage/Disadvantage of Top-down Method

Advantage: doesn’t need liquidity prem

Disadvantage: complexity of deriving & adjusting reference portfolio rate

*Opposite for bottom-up

Ex of Credit Risk

Default risk

Downgrade risk

What is considered risk-free?

Gov bonds

Liquidity Prem → Combined Approach

• Top-down Discount Rate = Ref Portfolio Rate - Credit Risk - Market Risk

  • Market risk = 0 if only bonds

• Ind Asset Liquidity Prem (ALP) = Top-down Discount Rate - Risk-free Rate

• Liquidity Prem = r x ALP + c

Contract Features that affect Liquidity

Exit Costs

• Ex: surrender penalties

• Higher = less liquid

Inherent Value

• Ex: payments the contract holder expects to receive

• Low inherent value = more liquid

Exit Value

• Large portion of inherent value paid @ exit = more liquid

Less liquid = _____ liquidity prem

Higher

Types of Insurance Contract Liabilities

Liability for Incurred Claims (LIC)

Liability for Remaining Coverage (LRC)

• More liquid → no claims occurred yet so easier to cancel

Basis for Varying Liquidity → LRC vs LIC

LRC: ability to cancel before expiry & receive value w/o significant exit costs

LIC: ability to obtain exit value in advance of “normal” payment dates

• Direct → ability of policyholder

• Reinsurance → ability of purchaser of reinsurance

Reference Curve

standardized yield curve used for comparisons in the unobservable period (30+ years)

Locked-in Yield Curve

Determined at initial recognition of group of contracts OR @ date of incurred claims

Used when:

• PAA approach w/ significant financing component

Where are insurance expenses reported in the Income Statement?

• Insurance service expense

• Insurance finance expense

Insurance Finance Expense

Change in carrying amt of group of insurance contracts from effect & changes in:

• TVM

• Financial Risk

Unwinding of Discounts

Diff between discounting CFs to beginning vs end of period

• Unwinding = Ending CF - Opening CF

Unwinding of Discounts → 3 Methods

Constant Yield Curve

• Uses same discount curve @ beginning & end of period

Unwinding using Spot Rates

• Ending discount curve = beginning discount curve shifted by 1 period

Expectation Hypothesis

• Term structure of interest rates is solely determined by market expectations of future interest rate changes

Unwinding → What’s the Ending discount curve for first year?

0%

• Ending disc CF = Undisc CF

Why can’t insurer use own assets as Reference Portfolio?

Diff in Liquidity between Insurer’s Assets vs Insurance Contract Liabilities:

• Insurers usually invest in liquid assets

• LIC is illiquid due to inability to obtain exit value before normal payment dates

Benefits of using single Liquidity Curve for both LIC & LRC

• Fewer curves to manage → could reduce # of curves by half

• Operationally simpler bc less calculations