Valuation and Capital: Segregated Fund Guarantees

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Valuation and CapitalSegregated Fund Guarantees

• Workshop on Options in Financial Products
• Fields Institute December 8, 2000
• Allan Brender, OSFI

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Actuarial Valuation of Liabilities

• The object of valuation of actuarial liabilities
  is not to determine a market price.
• Provision sufficient to meet policy liabilities
• Cash flows contingent upon uncertain future
  events over a long term
• Assumptions about the future include margins for
  adverse deviations

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Actuarial Valuation of Liabilities

• Actuarial liabilities represent an apportionment
  of the companys assets required to satisfy
  obligations to policyholders.
• Assets are segmented to back specific portfolios
  of business.
• Insurers investment policy is long term, buy and
  hold, and built around ALM.

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Actuarial Valuation of Liabilities

• Policy cash flows are discounted at the yield
  earned on the supporting asset portfolio, or
• The actuarial liability is equal to the statement
  value of the supporting asset portfolio.

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Actuarial Valuation of Liabilities

• Why not use market interest rates?
• With market interest rates, separate provision
  would be required for asset/liability mismatch.
• When insurance portfolios do trade, the trade
  usually involves transfer of the supporting asset
  portfolio.

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Actuarial Valuation of Liabilities

• Based upon projection of all relevant cash flows
• Use a variety of economic scenarios
• Policy cash flows may be sensitive to the
  economic scenario
• Requires dynamic investment policy

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Actuarial Valuation of Liabilities

• Assume economic scenarios are generated
  stochastically.
• We obtain a distribution of the cost of meeting
  obligations to policyholders.
• We use this distribution to determine both the
  valuation of the liability and required capital.

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Actuarial Valuation of Liabilities

• How do we allow for economic uncertainty in the
  liability valuation ?
• Use the risk-neutral (Q) measure and set the
  liability value equal to the mean, or
• Use the realistic (P) measure and set the
  liability value at some point in excess of the
  mean.
• Actuaries choose this approach

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Segregated Fund Guarantees

• Individual seg fund product is similar to a
  mutual fund.
• A seg fund is required when the return to the
  policyholder is directly related to a specific
  block of assets (ICA).
• Guarantees of return of at least 75 of premiums
  upon death or maturity are required by provincial
  securities laws.

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Segregated Fund Guarantees

• OSFI requires (1971)
• Guarantees not to exceed 100 of gross premiums
  (investments)
• Maturity period of at least 10 years
• Liabilities for seg fund guarantees to be
  established in an insurers general fund

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Segregated Fund Guarantees

• Initially, all seg funds carried 75 guarantees
  and maturities at a high (retirement) age.
• In the mid-1980s, one large insurer moved to
  100 guarantees.
• In the mid-1990s, the market heated up, offering
  10 year maturity periods and resets.

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Segregated Fund Guarantees

• In the mid and late 1990s, we had
• low policy liabilities
• no capital requirement
• for these guarantees
• in spite of
• results of the U.K. Maturity Guarantees Working
  Party
• unfolding experience in Japan

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Segregated Fund Guarantees

• OSFI and the Canadian Institute of Actuaries
  (CIA) both expressed concern over the situation.
• In 2000, the CIAs Task Force on Segregated Fund
  Guarantees developed an approach to liability
  valuation and required capital.

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Segregated Fund Guarantees

• The Task Forces approach is through projection
  of cash flows under stochastically generated
  scenarios, to generate the distribution of costs
  of these guarantees.
• The resulting distribution is strange all
  tail with a large probability mass at 0.

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Segregated Fund Guarantees

• The Task Force considered a variety of economic
  models.
• Not wishing to choose among them, the Task Force
  developed calibration criteria for the various
  models to ensure reasonably thick tails.

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Calibration Maximum Returns
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Segregated Fund Guarantees

• An interesting new model is the Regime Switching
  Lognormal Model developed by Prof. Mary Hardy of
  the University of Waterloo
• Six parameters
• Makes maximal use of calibration points

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Segregated Fund Guarantees

• Two levels are specified in the distribution
• The first for the liability value
• The second for the total of liabilities and
  required capital
• Levels are specified in terms of the Conditional
  Tail Expectation at the xth percentile, CTE(x)

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Capital Requirements

• OSFI has selected CTE(95) for the total of
  liabilities and required capital.
• Required capital is subject to the usual MCCSR
  multiplier.
• There is a phase-in over 2000-2001.
• For 2000, required capital is to be determined
  through a factor-based formula.

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Use of Internal Models

• If internal models are used to determine capital
  requirements, these will be subject to a regime
  similar to that applied to banks models for
  determining capital for trading risk.
• Audit of models by OSFI
• Required risk management program with oversight
  by OSFI

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Use of Internal Models

• Credit for dynamic hedging requires modelling of
  the hedging activity.
• The economic scenario generator will have an
  underlying P-measure.
• It must incorporate a Q-measure generator to
  price hedges at future time points within any
  scenario.

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Use of Internal Models

• Credit for dynamic hedging requires modelling of
  the hedging activity.
• Hedges will increase costs in all scenarios.
• Hedge pay-offs in unfavourable scenarios will
  reduce costs.

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Valuation and CapitalSegregated Fund Guarantees

• Allan Brender
• abrende_at_osfi-bsif.gc.ca