23. Reserves and Solvency Capital Requirements Flashcards
Reasons for calculating reserves
- determine liabilities for published accounts
- determine liabilities for solvency accounts
- determine liabilities for internal management accounts
- assist in premium rating
- value insurer for merger and acquisition (EV)
- influence investment strategy
- assist with assessment of reinsurance arrangements
Purpose for estimating liabilities vs basis used
Published accounts
- true and fair approach, consistent with relevant accounting principles
- assumptions usually on prudent side of BE
Solvency accounts
- most prudent assumptions appropriate to protect policyholders
Internal Management Accounts
- BE assumptions (BE with small margins against parameter error) usually most appropriate to give realistic view of financial condition of the company
Setting premium rates
- BE basis likely to be used
- assumptions slightly prudent to avoid premiums too low
Merger or acquisition
- likely to be BE; optimistic side if selling, prudent side if buying
Investment strategy
- BE assumptions usually used to insurer can select appropriate assets to meet liabilities
Reinsurance agreements
- BE assumptions usually used to give realistic view of appropriate reinsurance options
Types of reserves
Long-term insurance
- reserves for in-force policies
- claims reserves (including IBNR)
- option reserves
- for group contracts (UPR, URR)
Short-term insurance
- unearned premium reserves (UPR)
- unexpired risk reserve (URR)
- incurred but nor reported claims reserve (IBNR)
- claims in transit reserve
- outstanding claims reserve
- incurred but not enough reported claims reserve (IBNER)
- equalisation/ catastrophe reserve
Methods for calculating reserves for health and care
- case estimates
Generally more important for smaller PMI insurer, due to greater potential impact of a large claim. Involve an experienced claims manager estimating the ultimate outgo for each case separately, taking into account: - procedure type, hospital, surgeon/ consultant, policy coverage, age, gender, past claims history, current levels of medical inflation
- statistical estimates
Appropriate for homogeneous claims where the portfolio is large enough and experienced is deemed stable - estimate outstanding claims for cohorts of policies based on historical trends and patterns and adjusting for known or anticipated future trends
Statistical estimates
Main groups:
- chain ladder methods
- average cost per claim methods
- loss-ratio methods
- blends, combinations - e.g. BF
Statistical methods of estimating outstanding claims might be impaired by errors, ommissions, distortions in the data
Bootstrapping
- process of deriving additional information about statistical properties based only on the data
- can be used to estimate the variance of the projected IBNR reserves
Assumptions underlying bootstrapping the chain ladder model
- run-off pattern is the same for each origin period
- incremental claim amounts are statistically independent
- variance of incremental claim amounts is proportional to the mean
- incremental claim amounts are positive for all development period
Principles of setting solvency reserves (BL)
- reserve should cover all liabilities arising from the contracts
- reserve should be calculated prudently
- reserves should take credit for future premiums if contractually due to be paid
- valuation should be prudent, not best estimate, and to the basis should contain margins
- valuation of liabilities should be consistent with valuation of assets
- appropriate approximations or generalisations should be allowed
- interest rates used for calculating reserves should be chosen prudently, taking into account the currencies, yields and reinvestment yields on the assets
- elements of the statistical basis: demographic, persistency, expense assumptions used should all be prudent (expenses can be on an ongoing business basis)
- if the valuation method itself defines the amount of expenses assumed (e.g. net premium method), then the amount implied must be no less than a prudent estimate of the relevant expenses
- valuation calculations conducted over time should not suffer discontinuities arising from arbitrary changes to the basis
- valuation bases and method should be disclosed
- valuation method used should recognise the emergence of profit appropriately over the policies’ lifetimes
- allowance for expenses should allow for possibility of ceasing to write new business, if that would increase the reserve
Solvency capital requirements
- used to protect policyholders from under-reserving (adverse future experience relative to reserving basis assumptions)
- drop in asset values
Interplay between reserves and SCR
- strong reserving, small SCR
- weak reserving, large SCR
Risk-based capital
- establish extra amount of capital required to protect insurer from the broad risks (under-reserving, drop in asset values)
- the level of solvency capital required under regulation may be specified as a formula, or based on a risk-measure such as Value-at-Risk
Value-at-risk (VaR) approach
- example of risk-based solvency capital requirement approach
- normally expressed at a minimum required level (e.g. 99.5%) over a defined period (e.g. 1 year)
- the insurer calculates the amount of capital it needs so its assets will exceed liabilities in one year’s time with probability
- can be calculated by subjecting the supervisory balance sheet to stress tests (on each of the identified risk factors, at the defined confidence level, over the defined period)
- applying stress tests to each different risk factor gives a capital requirement for each separate risk in isolation
- aggregated capital requirement combines the separate tests to allow for any diversification benefits that exist between the various risks
- may be done through use of correlation matrices/ copulas
- risks are not perfectly correlated, so the insurer can hold a smaller amount of capital to reflect diversified portfolio of risks it is exposed to
- separate allowance made for effects of non-linearity and non-separability of individual risks
99.5% confidence level is equivalent to looking at 1-in-200 yea events, and it is difficult to extrapolate such events from only a few decades of actual data
Market-consistent (fair value) valuation for reserves
- market-consistent liability value is the price someone would charge for taking ownership of the liability, in a market where such liabilities are freely traded
- to determine market-consistent value, future unknown parameters and cashflows are set to be consistent with market values
Example: immediate needs LTC
- expected cashflows, allowing for mortality projected
- the CFs may be taken as the maturity proceeds of a series of ZCBs “risk-free” of matching term
There are two approaches:
- replicating portfolio approach: devise a portfolio of ZCBs whose cashflows exactly replicate those of the liabilities, and the current market price of the replicating portfolio becomes the market-consistent value of the liabilities
- discounted CF approach: the cashflows may be discounted at current risk-free rates of interest
- future investment returns are based on risk-free rates of return (irrespective of assets actually held)
- discount rates are also based on risk-free rates
- risk-free rates may be determined based on government bond yields or on swap rates
- could use different discount rates for cashflows at different durations
- may be appropriate to make a deduction to risk-free rate to allow for credit risk (take credit for illiquidity premium, higher discount rate –> lower liabilities, better solvency position)
- generally only appropriate to use swap rates if there is a sufficiently deep and liquid market in the country
Risk margin
- market-consistent methodology only appropriate for cashflows that are of known and certain amounts
- difficult to make market-consistent assumptions for some elements of the basis: morbidity, expenses, persistency
- approach is to project the expected future amounts and then discount as if the cashflows were known and certain
- adding a risk margin to the best estimate value of liability (to allow for possibility that the liability turns out worse than expected - from the purchaser perspective)
- risk margin reflects the compensation required by the market in return for taking on those uncertain aspects of the liability cashflows
- a margin could be added to each assumption or a cost-of-capital approach could be used
Active and passive valuation
Passive
- valuation methodology relatively insensitive to changes in market conditions, valuation basis updated relatively infrequently
- example: net premium valuation, assumptions may be “locked-in”
-easy to implement, less subjective
Active valuation
- based more closely on market conditions, with assumptions updated frequently
- more informative ito understanding impact of market conditions
- examples: market-consistent valuation, risk-based capital approach
