Part 5

Question 1

How to price Options and guarantees

Answer 1

1. Option pricing techniques
   
   1. An option pricing approach assess the value of a guarantee as the market price of an option or other derivative that the insurance company could acquire to hedge the risk associated with the guarantee
   2. This guaranteed fixed minimum maturity benefit corresponds to a put option on the assets in the unit linked funds
   3. As the guarantee applies only at one point in time a European put option would be suitable
   4. The insurance company should select options with maturity dates as close as possible to the maturity dates of the policies with the maturity guarantee
   5. The insurance company should select options that most closely represent the assets within the unit funds for e.g. market equity or bond indices
   6. The strike price of the options should correspond to the fixed minimum maturity guarantee amount
   7. When the determining the notional amount required, allowance can be made for the fact that not all existing policies will reach the maturity date i.e. the number of options contracts required can be reduced by allowing for expected mortality and persistency
   8. The market consistent value of the liability is the market price of these options provided they are traded in a deep and liquid market ix. If such market values do not exist then an alternative approach is needed to value them e.g. black Scholes
2. Stochastic simulation of investment performance
   
   1. Appropriate selection of model points that represents the policies managed by the company
      
      1. Benefit type
      2. Size
      3. Age
   2. Unit funds should be projected realistically, net of all charges, allowing for deaths and withdrawals iii.
   3. Key assumptions will be
      
      1. probability distribution used to model
      2. the investment return and mean and variance.
      3. These should vary for different funds available
   4. Should take into account expected policyholder behaviour i.e. higher withdrawal rate should be assumed when the guarantee bite. Withdrawal rate should be dynamically linked to the fund performance
   5. At each future time, the excess of the guaranteed value over the unit fund, where positive, is the simulated guarantee cost for each run
   6. The present value of the liability can be determined by multiplying the simulated cost of exercising the option by the assumed surrender rate at each future time, and then discounting at a suitable discount rate
   7. Repeated simulation will generate the probability distribution of the present value of the cost of option
   8. Charge premium having a present value which reflects this cost of providing the guarantee this could cover the cost of guarantee with a suitable probability
   9. Sensitivity tests should be performed e.g. to the choice of probability distribution and to different deterministic assumptions including mortality rates

Question 2

How to use simulation to evaluate the surrender the value

Answer 2

1. A stochastic model is used to simulate the future price of assets in the unit fund
2. A valuation needs to be market consistent a risk free return will be used
3. These risk free rates may be determined based on government bond yields
   
   1. Or on swap rates if there is a sufficiently deep and liquid swap market in the country concerned
4. In either case an appropriate deduction would be made to allow for credit risk
5. A large number of simulations would be needed to obtain reliable results
6. Investment return volatilities will be required and these should reflect the actual assets in the unit funds
7. The starting point for the mortality and persistency assumptions would be best estimate
8. It may be decided to include a risk margin in each of these assumption due to the inherent uncertainty
9. Alternatively an overall risk margin could be used to arrive at a market consistent value e.g. using cost of capital approach
10. For each simulation, the model needs to calculate the excess of the fixed guaranteed benefit over the projected unit fund at the maturity date
11. The cost at maturity is then set as the higher of this excess and zero
12. The present value of the guarantee liability can then be determined by discounting these simulated costs of guarantee
13. This discounting would use the risk free rates
14. A large number of simulations will be run in order to generate a distribution of the present value of the cost of the guarantee
15. The market consistent liability is the average cost across all these simulations
16. A large number of simulations is needed in order to obtain a reliable estimate

Question 3

Main types of reinsurance

Answer 3

1. Original terms - once everything is signed nothing changes
   
   1. Original terms reinsurance involves sharing all aspects of the original contract
   2. The contract is split between the insurer and reinsurer in a fixed proportion and any claim is split in that same proporiton
   3. The cedant will provide the reinsurance company with the premium rates it is using for the particular class of business it wishes to reinsure
   4. The reinsurance company will determine the rates of reinsurance commission it is prepared to pay to the cedant for the business
2. In determining the reinsurance commission, the reinsurer will have regard to
   
   1. its likely future experience
   2. the quality of the cedant’s underwriting.
   3. It will also want to make a profit on the business
3. The reinsurance commission will usually cover -in respect of the reinsured portion of the policy
   
   1. the commission that has been paid by the cedant
   2. part or all of the cedant’s other initial expenses
4. The amount to be reinsured can be on an individual surplus or a quota basis
   
   1. Types 1) Quota share
      
      1. Specific percentage
      2. Individual surplus
         
         1. Retention level
5. Excess of loss
   
   1. Stop loss
   2. Catastrophe
6. Financial reinsurance
   
   1. Risk reinsurance premiums
      
      1. A loan is presented to the insurer in the form of initial reinsurance commission as part of the risk reinsurance agreement
      2. The repayments are spread out over several years and are added to the reinsurance premium
      3. The reinsurance takes in account the expected future lapse experience of the insurer when determining repayments
      4. The loan is effectively repaid by the insurer from its future premium receipts. It does not set up any additional liability for the repayments, as they are only payable for as long as the policy remains in force
      5. The assets increae by the amount of the reinsurance commissions, the liabilities are unaffected, and therefore the net assets of the insurer increase
   2. Reinsurer sets premiums to accept the risk
      
      1. Risk premium + expenses +profit
      2. The cedant reinsures part of the sum assured. I.e. the excess of the benefit payable over the reserve on the reinsurers basis
      3. Reinsurer determines the its risk premium rates by assessing the likely experience of the business it is to reinsure and then adding expense and profit margins
      4. It may guarantee these rates for the term of the policy or may review them every year
      5. There are 2 ways in which the amount to be reinsured can be specified
         
         1. Individual surplus - the reinsured amount is the excess of the original benefit over the cedant’s retention limit on any individual life
         2. Quota share - a specified percentage of each policy reinsured
         3. This is suitable for unit linked business 1) Original terms could be difficult to obtain 2) Unit fund fluctuate and reinsurer will have to pay a proportion of the benefit and match the performances of the unit fund 3) This is appropriate if it is new business 4) Reduce NB strain e. Financial reinsurance i. Risk Premium Reinsurance 1) Loan is presented as Reinsurance commission 2) Repayments are spread out over a number of years and is added on top of reinsurance premiums ii. Contingent loans 1) VIF refers to the margins applied that are above the realistic assumptions 2) This loans are provided and repayment are contingent on making profit f. Facultative and obligatory reinsurance

Obligatory means that the writer will have to reinsurer it or that reinsurers have to take on the risk. This may require a treaty

1. This maybe advantageous because insurance companies do not have to refer back to the reinsurer
2. Facultative means that companies have more freedom

Question 4

Why reinsurance

Answer 4

1. Limit total claims pay out
2. Limit total amount paid out on a particular claims
3. Reduce insurance parameter risk
4. Reduce the claim pay out fluctuations
5. Receive technical assistance
6. Reduce new business strain
7. Increase profit
8. Reduce overall capital requirements
9. This could be the best use of limited capital reserves
10. Allow aggregation risk that the cedant cannot manage Separate out different risks Smooth results Avoid large losses Diversification Limit exposure to risk (single event, accumulations) Increase capacity to accept risk Financial assistance - Product design, assumptions and pricing Expertise

Question 5

Process of underwriting

Answer 5

1. Medical evidence
   
   1. Questions on proposal form
   2. Usually this would be enough but there could be “medical limits” based on questions
   3. Doctors report
   4. Medical examination
      
      1. Look at basic information such as weight and height
      2. Specialist medical tests
      3. May include X ray
   5. Other evidence
      
      1. Application occupation
      2. Leisure pursuits of the applicant
      3. Country of residence
   6. Financial underwriting
   7. This is to ensure that policyholders can afford the premiums
   8. May gather information such as income d. Claims underwriting
      
      1. Check if pay out is required e. Interpretation. The steps required are
      2. Proposal forms are reviewed
      3. Specialist will review the application form
   9. Specification of terms
      
      1. An increase in premiums will be applied that is commensurate with the degree of extra risk
      2. A deduction is made from the benefits iii. An exclusion clause maybe added ot the contract
         
         1. This is the least popular since it might not fulfil the policyholder’s requirements
         2. Difficulty in proving the that a claim falls under “special” term

Question 6

Reconcillation checks

Answer 6

data at previous + business come into books - business gone off = data at current There are

4 main types

1. Number of contracts
2. Benefit amount
3. Premiums payable
4. Number of units allocated split by fund
5. The amount of attaching bonus

Question 7

What are the Consistency checks

Answer 7

1. Comparisions with previous
   
   1. The average sum assured for each class of business should be consistent with the figure for the previous investigation
   2. The average premium for each class of business should be consistent with the figure for the previous investigation.
   3. The ratio of the basic sum assured (or equivalent benefit) to the premium payable, for each class of regular premium contract, should be consistent with the figure for the previous investigation.
2. Consistent For unitised contracts, a check that the number of units purchased by premiums are consstent with the corresponding revenue account items.
3. For unitised contracts,
   
   1. check that the number of units encashed to pay benefits are consistent with the corresponding revenue account items.
   2. For unitised contracts, check that internal unit movements, for example the amounts of charges encashed, are consistent with the surplus emerging during the year.
   3. The ratio of the total bonus to the total sum assured should be sensible for the class of business, and consistent with the previous investigation.
   4. Sense check
      
      1. The average sum assured for each class of business should be sensible.
      2. The average premium for each class of business should be sensible.
      3. The ratio of the basic sum assured (or equivalent benefit) to the premium payable for each class of regular premium contract should be sensible.
      4. Other The persistency rates should be sensible for each class of business, and consistent with the previous investigation, as a check on the movements data’

Question 8

Check on Mortality

Answer 8

1. The company should ensure that it is maintaining all the data items required and that they can be accessed in the required format.
2. As this is an annual investigation, a reconciliation should be performed of the current data with those used for the previous mortality investigation.
3. To do this check, the term assurance policy data should first be grouped by rating factor, for example by year of entry and age.
4. Using data similarly grouped for policies that have come onto the company’s books (new business) and gone off between the dates of the two investigations, the following check is made for each group: the number of contracts
   
   1. the sum assured
   2. the office premium.
5. data at previous + policies on - policies off = data at current
6. For term assurance policies, the company could perform this check for:
7. the number of contracts the sum assured the office premium.
8. The systems for producing the movements data should be checked periodically to ensure that they are working correctly and that the staff involved are following the procedures laid down.
9. The movements data should also be checked against any appropriate independent accounting data, especially with regard to benefit payments, ie death benefits for term assurances.
10. The company should compare an extract of the computer held data with the information in any paper administration files.
11. This can be done on a spot check basis by randomly selecting a number of policies.