Butsic: Solvency Measurement Flashcards
Technical insolvency
When obligations exceed assets
When solvency regulation would not be necessary
If there was a perfectly efficient market
Why solvency protection is desirable
Information asymmetry; less informed personal lines customers
Desirable features of a RBC Method
- Standard should be the same for all classes
- Should be objectively determined (two identical insurers should have same RBC
- Must be able to discriminate betwen quantifiable items of meaningful value that differ materially in their riskiness
(Note: risk element must be a balance sheet quantity)
When risk is present for a balance sheet item
When future realization of the item can be one of several values, but particular outcome is currently unknown
Why probability-of-run criterion is inadequate to express policyholder exposure to loss
It ignores the severity of the ruin
Policyholder deficit
Expectd value of the difference between the insurer obligation and the actual amount paid
EPD where assets are certain, discrete
EPD where losses are certain, discrete
EPD where assets are certain, continuous
EPD where losses are certain, continuous
Assuming normal distribution, EPD ratios
If CV is the same, to make dA = dL
More capital (per unit of assets) is required for assets than for losses (per unit of losses)
When normal distribution is reasonable approximation for variation of aggregate incurred losses
When individual losses occur independently of each other (i.e. non-CAT property insurance)
When lognormal distribution is reasonable to approximate variation of aggregate losses
For correlated events
Advantages/Disadvantages to lognormal distribution
A: Negative values impossible
A: Skewness of outcomes appears to accord with observed results
D: Sum of two lognormals only approximately lognormal
Assuming lognormal distribution, EPD ratios
Capital requirement, normal vs. lognormal
Lognormal requires less than normal
Due to skewness of lognormal (asset values cannot be negative)
Probability of large losses higher under normal distribution
Accounting treatment for solvency risk measurement
Should directly reveal realizable value variations
Market-value accounting is suitable since failure results in liquidation or repurchase, which happen in market transactions
Limits of accounting book value definition of capital
Accounting bias (current recorded value differs from current realizable value
SAP allows insurers to consistently over- or under-value financial statement elements (i.e. not discounting loss reserves)
SAP and GAAP inconsistent
Time-dependent nature of risk
Variance will increase through time even though mean could remain constant or decrease
Use variance per unit of time instead
Expected insolvency cost over time
Increases with length of time required to pay loss, since spread of possible loss values widens
Key requirements to keeping consistent level of policyholder safety
Know time-dependent nature of future realizable values
Insurer can liquidate assets/liabilities at each evaluation point
Insurers will add capital when needed
EPD for liability risk element paired with riskless assets
Equivalent to a call opten on the losses with exercise price equal to value of assets at the end of th eyear
EPD for asset risk element paired with riskless liability
Equivalent to a put option on the ending assets
Mean and variance of capital with two normally distributed assets or liabilities
Square root rule for aggregate risk capital
If two items are on opposite sides of the balance sheet
Change the correlation sign
Key results of Butsic
- Relevant measure of solvency is PV of EPD as ratio to expected loss
- Market value removes measurement bias
- Longer time to realization, greater the risk
- Capital is not required now for distant contingencies
- RBC < sum of all RBC elements
5b. Knowing correlation between risk elements super important
