AS3303 General Insurance

Question 1

i) You are carrying out a claims and exposure analysis exercise for your household insurance policy for the accident year 2020. The purpose of the work is to update the premium assumptions for one group of policyholders (the “rating group”) who live in houses that are over 30 years old, have more than 4 bedrooms and contents worth more than £50k.

The policy administration system is old and assumes that any policy that renews during 2020 will add a whole sum-insured-year to the exposure table. The exposure value for the rating group from this system is £24.6m sum insured years over the period.

Your manager has confirmed that the exposure table your policy system produces does not allow for lapses, cancellations or endorsements. They have asked you to adjust it, given the following information, noting that each of the policies below will have contributed a whole year of exposure.

Policy 1: Renewed on 1 December 2019 and has a sum insured of £140k and lapsed on 1 May 2020

Policy 2: Renewed on 1 March 2020 and has a sum insured of £230k and lapsed on 1 November 2020

Policy 3: Has a sum insured of £190k and took out their policy on 1 February 2020 but cancelled on 1 September 2020 when they moved house

Policy 4: Renewed on 1 June 2020 and notified you that they have had an extension to add a fifth bedroom to their house on 1 April 2020 and they estimate their sum insured is now £205k

Policy 5: Renewed on 1 April 2020. Was built on 1 June 1990 and has a sum insured of £312k

Policy 6: Renewed on 1 November 2020. Notified you on 1 July that their prize painting has been recently shown to be a fake so their contents value is now £30k. Their sum insured is £430k

Assume no other policies lapse, cancel or endorse their policy and all other in-force policies renew during the year.

Calculate the revised exposure value for this rating group and explain your answer. (8 Marks)

ii) The claims system is also old and reports that there were 7 claims arising from this rating group totalling £3.4m. Your manager has said you should cap any claims that are in excess of £400k since these will be taken care of by your reinsurance programme. They note that the claims figures include:

A claim for policy 26 a large mansion built in 1688 which is for £2.1m

A claim for policy 6 for £340k

The policy numbers above are from the same system as those in parti). Calculate the revised claim amount and claim numbers for this rating group and explain your answer. (3 Marks)

iii) Your new premium rates will come into force from 1 September 2022 and will be used for 18 months before they are reviewed again. All policies are annual (in-force for 12 months). You are told:

In 2020 claims were paid on average 5 months after occurrence, but in 2022 and beyond due to a new process you expect this to fall to 3 months.

Industry analysis suggests that claim frequency will increase from 2020 and beyond by 5% p.a. due to a predicted rise in theft. This analysis also suggests that claims inflation has been constant at 8% p.a. throughout 2020 and this is likely to continue for the foreseeable future caused by wage increases for builders and an increase in the cost of building materials. A separate report suggests that house price inflation will be zero for the next few years due to more new housing coming on to the market.

Calculate the risk premium for this rating group expressed as a percentage of sum insured, stating your assumptions. (10 Marks)

iv) Explain what other factors you would consider to recommend the new premium rate for this rating cell. (4 Marks)

[Total 25 marks]

Question 2

i) Define Unearned Premium Reserve (UPR). State a method that a modern computing system could use to calculate this exactly for an individual policy facing a uniform amount of risk during the year. State any assumptions underlying this method. (3 Marks)

ii) State what an Additional Unexpired Risk Reserve (AURR) is and its purpose. (2 Marks)

iii) A (fictitious) Lloyd’s syndicate Mercury offers hurricane risk reinsurance to a US direct insurer Coastline Protection Ltd, this policy only covers property damage due to hurricanes, the premium is $2.5m. Coastline Protection Ltd renews its policy on 1 May each year so it can view the early hurricane season forecasts. The hurricane season is deemed to start on 1 June and end on 30 November each year, Mercury recognises the non-uniform nature of this risk and assumes the risk is zero outside of this period and then follows the following schedule when calculating their UPR (all expressed as a percentage of annual risk): June 5%, July 15%, August 20%, September 30%, October 25%, November 5%. Mercury shows the UPR gross of Deferred Acquisition Costs (DAC) and then holds a DAC asset in its accounts.

a. Mercury is calculating its quarter end management accounts (as at 30 September). Calculate the UPR it should hold for its exposure to Coastline Protection Ltd. (2 Marks)

b. Mercury pays 30% commission to a Lloyd’s broker for placing the business with them, the broker carries out all acquisition activities so there are no other initial expenses. Calculate the asset for Deferred Acquisition Costs that they should hold in their accounts with respect to Coastline Protection Ltd. (1 Mark)

c. The exposure manager at Mercury has informed the management that a La Nina is forecasted to start from 1 September until 31 October which is likely to increase hurricane risk by 10% per month in that period. Calculate the AURR they should hold in respect of Coastline Protection Ltd, ignore any premium loadings or expenses other than initial expenses. (2 Marks)

d. Mercury suffers a major loss on 1 October and has to go into run-off (i.e. it closes to new business). It only had one member and their Funds at Lloyd’s can only pay a proportion of the loss. They have decided not to continue at Lloyd’s. Explain why Coastline Protection Ltd may still be paid in full for any losses. (1 Mark)

iv) Define anti-selection (1 Mark)

v) A new hurricane forecasting technique has been found which has significant prediction skill in forecasting the number and likely landfall location of hurricanes in the coming season. The forecast only has skill after 1 April each year. Explain how this might affect Mercury in future and what they can do in response and comment on whether this is an example of antiselection and why. (7 Marks)

vi) The Head of Innovation at Mercury intends to create a new direct insurance product using the new hurricane forecast which is aimed at US cities. The product will be available to purchase from 1 January until 30 March, only, and will pay out to cities that are forecasted to be at increased risk of hurricane landfall. Describe the steps that the Head of Innovation should follow to set the product development team up for success. Comment on how “Failure” could be defined for this project. (6 Marks)

[Total 25 Marks]

Question 3

i) Give the pros and cons of using Scenarios as a basis for catastrophe modelling and exposure monitoring. (4 Marks)

ii) List 8 different types of event other than terrorism that would lead to multiple insurance claims from a single cause. (4 Marks) iii) You work for ABC insurance PLC in their capital modelling department and have been asked to calculate the updated property loss for their terrorism scenario. The scenario details are:

- A conventional 1 tonne bomb is exploded in City X in the UK

- all buildings within 100m of the epicentre suffer 90% damage to Total Insured Value

- all buildings outside 100m but within 300m suffer 40% damage

- any buildings within a 300-500m radius suffer 10% damage

- any buildings constructed before 1985 have less protection and suffer an additional 10% of damage

- Assume this is the only terrorism event in the year and there are no other major property catastrophes in the year

a) Define the Ground Up Loss (GUL) and calculate it for all properties in your portfolio and state the total GUL. (6 Marks)

b) Define the Gross Loss (GL) and calculate it for all properties in your portfolio and state the total GL. (6 Marks)

c) You have asked ABC’s Reinsurance team to inform you of any reinsurance that might be relevant to the scenario, they have responded with the following information.

- Facultative reinsurance

- contract A purchased for the following buildings:

- Building D: Deductible: 50m Limit: 200m

- Building F: Deductible: 100m Limit: 300m

- Building I: Deductible: 100m Limit: 400m

- Excess of Loss policy B covering all properties in the UK, the facultative policies Inure to the Benefit of this policy.

- deductible: 200m

- Limit: 300m

- Single event only: reinstatement premium $ 6m: the company will choose to reinstate.

Define the Net Loss (NL) and calculate it in total for scenario. (4 Marks)

d) Define the Final Net Loss (FNL) and calculate it in total for the scenario. (1 Mark)

[Total 25 marks]

Question 4

i) Define the term Incurred But Not Reported (IBNR) and explain why insurers must hold a reserve for this. (2 Marks)

ii) Define the term Case by Case reserve and say, with your reasons, whether you believe an insurer should base their reserves solely on this method. (5 Marks)

iii) You work for the actuarial team in a small insurer. A senior actuary has given you Total claims costs and the number of claims for various years and says “this data, which contains claims handling expenses as well as claims payments is ready for you to use”. Calculate an undiscounted outstanding claims reserve for each accident year and the total reserve using the average cost per claim method, stating any assumptions and concerns you have with the data and how you might address these. The phrase NaN represents an empty field in the data. (13 Marks)

iv) Give reasons why the average claim costs in development periods 3 and 4 might be higher than the other periods. (4 Marks)

v) You present the results to the board and the marketing director says “you have clearly made a mistake some of your ‘expected’ claims numbers are not whole numbers – we can’t have a fraction of a claim!”. How do you respond to them? (1 Mark)

[Total 25 marks]