Fair valuation: theoretical and practical issues in the French context

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Fair valuationtheoretical and practical issues
in the French context

• Actuarial Colloquium
• Copenhague, 1st June 2001

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• Alain Tosetti
• Commissaire Contrôleur Général in charge of
  relations with actuaries within the French
  Insurance Supervisory Authority
• Aymeric Oudin
• Head of the Insurance Market and Product Division
  at the French Treasury (Ministry of Finance)
• Jean Berthon
• Délégué Général of the Institute of French
  Actuaries

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Presentation

• Introduction on valuation prudential
  principles in French insurance, focusing on fair
  valuation issues in both general life insurance
  (A. Oudin)
• Some specific issuesboth theoretical
  practical, illustrated by considerations on
  embedded options in French life policies (A.
  Tosetti)
• Floor guarantee development of French
  Actuaries works on the last of those options (J.
  Berthon)

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1st theoretical issue Can a single fair value
exist?

• Prudential regulation reflects classical economic
  tools for solving classical conflicts between
• StockHolders who put initial equity E0
• and creditors (here PolicyHolders) who (as a
  whole) put in L0 (premiums), in order to
  receive later L1 L0 (1r)
• the company purchased A0 E0L0

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Can a single fair value exist? (2)

• the company purchased A0 E0L0
• SHs net payoff max (A1-L0 (1r), -E0)
• PHs net payoff min (A1-L0, rL0)
• SH bought a call, PH sold a put
• no reason for them to agree on pricing
• (cf. Dewatripont-Tirole book, G. Plantin thesis)

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Can a single fair value exist? (conclusion)

• 2 solutions
• an easy one 2 sets of accounts
• cf. US statutory vs GAAP
• a better one 1 set of accounts including
  information needed by everyone
• cf. European 1st directive

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Introduction

• Valuation and prudential principles
• in French insurance
• non Life
• Life
• contracts
• technical provisions
• Main issues of fair valuation (A. Oudin)

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Non life Contracts

• Freedom of tariff
• No control of contract prior to commercialization
• Specific regulation or industry organization-
  health- motor liability- building

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Life contracts (1)

• General conditions- No control prior to
  commercialization - Surrender value (low maximum
  penalty)- Participation minimum on two
  levels - contractual basis - company
  basis management decision, in practice good
  level and regular (no terminal  bonus)
•  Participating savings policies  represent 70
  of the French market

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Life contracts (2)

• Pricing- Mortality table regulatory or
  certified by an actuary- Maximum interest
  rate under 8 yr. Min.(4.5 , 75 10yr Tbond)
  over 8 yr. Min.(3.5 , 60 10yr Tbond)
  periodic premium Min.(3.5 , 60 10yr Tb.)-
  Loadings freedom

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Principles of valuation and supervision

• technical provisions gross of reinsurance,
  sufficient
• admitted assets covering the technical
  provisions (and other liabilities)
• EU solvency margin

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Non Life Provisions

• Principles sufficient, gross of reinsurance, no
  discount
• Provisions- for unearned premium ( for premium
  deficiency)- claims (incl. IBNR and expenses)-
  others equalization...

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Life Provisions

• Mathematical provisions- use pricing
  assumptions at inception (no lapse rate)-
  cannot be less that the surrender value- in case
  of durable adverse change must use new
  assumption (ex. annuities)
• Other provisions - provision for future
  expense- provision for unallocated
  participation- provision for insufficient
  investment yield

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Assets

• Historical cost for all investments For shares
  and real estate, global provision for
  depreciation
• Coverage of the technical provisions - List of
  admitted investments, limitations by category
  and issuer - Other admitted assets reinsurance
  recoverable (pledged assets), recoveries
  (limit), outstanding premiums (limit) ...

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EU Solvency Margin

• EU Required minimum- non-life max(16
  premiums, 23 losses)- 4 of PM (1 for unit
  linked)
• Available margin - Equity - Unrealized capital
  gains- Others preferred loans

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Fair Value

• Price for settling insurance liabilities ?- No
  market, agreement for portfolio transfer-
  Reinsurance is not observable
• Stochastic valuation of two components -
  Expected value of cash flows- Provision for risk
  and uncertainty (or MVM)
• Fair value of assets

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FV theoretical issues

• Does replicating portfolio approach include MVM?
• What unit of account for EV, MVM?
• Stochastic assumptions(of the entity, of the
  market?) - pattern of cash flows (incl.
  embedded options)- interest rate
• level of confidence of the FV (provision for
  risk and uncertainty)

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FV issues Pattern of cash flows

• Stochastic assumptions, for example- industrial
  risk, general liability- lapse rates- long term
  care- participation for life contracts
• Embedded options, for example- option for
  annuity- surrender value- floor guarantees

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B) Specific issues

• Theoretical and practical issues
• Participating contracts and theoretical issue
  on FV of Assets
• Loadings in reinsurance
• and theoretical issue on FV of Liabilities
• Valuation of embedded options
• annuity/ surrender value /floor guarantees

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Issue 1 Participating contracts

• 8 year Contract - guaranteed interest rate
  i3 - PHs participation 100 of realized
  gains - surrender value no penalty -
  assumptions no mortality, flat interest rate
  curve (j5 at t0)
• 2 accounting scenarios - Presently /Fair Value
• assumed lapse rate 0
• no deposit floor

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Issue 1 j stays 5

• Presently
• asset 1005
• liability 10032surrender v. 105
• unrealized p/l 0

• Fair value
• asset 1005
• FV of Liabilities (guarantee PHs
  participation)
• less than 105?
• accounts
• showing a profit?

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Issue 1 j jumps at 7 at t1

• Presently
• asset 1005
• liability 10032surrender v. 105
• unrealized loss 12

• Fair value
• asset 885
• liability ? surrender v. 105
• FV showing no loss in the accounts ?

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Issue 1 theoretical question

• In general, can accounting be different than
• adding Unrealised gains to Assets (today U
  disclosed, in annex to the accounts)
• Þ adding to the Liabilities at least
• 85 of U (policyholders share)
• 40 of 15 of U (taxes share
• can assets minus liabilities change without a
  major modification of policies

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Issue 2 general

• As said before, transactions on pure liabilities
  exist in reinsurance, but
• As loading proportional to ?
• Bs loading proportional to ?²/...
• Very different consequences
• for A, price(R1R2) price(R1) price(R2)
• for B, price(R1R2) lt price(R1) price(R2)
• Can FV go without agreeing on loading?

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Issue 2 general (2)

• prudent estimates not analyzed now in
• a best estimate component
• and a provision for adverse deviation
• as difficult as analyzing safe speed
• a speed at which one stay on the road one curve
  out of two
• (minus) a security margin component

extra research is needed
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Valuation of embedded options

• Side guarantees or embedded options
• capital /annuities option in classical
  policies
• guaranteed surrender value in modern
  policies
• floor value in new unit-linked policies

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Issue 3Capital /annuities

• in long term classical policies
• annuities very favorable to PH
• computed with obsolete mortality tables
• chosen of course by healthy PH
• problem forecasting PHs behavior
• at maturity,everybody chooses capital
• but things can change!
• cf. Olivier Arles and alii article

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Issue 4 Surrender v.

• Previous contract - guaranteed interest rate
  3 - for a 100 F premium PH can have
• 127 (capital) in 8 yr.
• or 103 in 1 yr., 106 in 2, (surrender v.)
• the insurer
• buys bonds (ex.5) to have 148 in 8 yr.
• a likely 2 differential to
• face adverse deviations
• hope for a profit (85 of it PHs share)

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Guaranteed surrender v. (2)

• If interest rates jump (ex. 7 after a yr.)
• rational PH would ask 103 surrender v.
• insurer owns bonds worth 88
• problem forecasting PHs behavior

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Issue 5 Floor guarantee

• in unit-linked policies, the insurer
• sells guarantees linked to units (such as stocks
  or building)
• buys those units
• will have probable profit (dividends,...) to face
  adverse deviations and hope for a profit
• every new policy with a floor guarantee

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Floor guarantee (2)

• floor guarantee
• in case of death
• some in case of survival
• diversity of pricing, not all prudent
• cf. Pricing of floor guarantee (S Merlus- 0.
  Péqueux for pricing as a financial product)
• one of the problems forecasting PHs behaviour
  (no experience!)

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Provisioning embedded options

• In introduction to J. Berthons
• presentation of the work of French
• actuaries on floor guarantees
• practical issue what is better
• provision financial pricing of the option
• or provision ? a stress test?