pricing for different covers

Discussion in 'SA3' started by NeedToQualify, Mar 12, 2008.

  1. NeedToQualify

    NeedToQualify Member

    Hi,

    I am a bit confused about what happens when for the same exposure we add more covers. e.g.

    Motor:
    1 contract (i.e. 1 vehicle-year)
    cover for 2 drivers
    Vs
    2 contracts (i.e. 2 vehicle-years)
    cover for 1 driver each

    Household:
    1 contract (SI 100,000)
    cover for fire and storm
    Vs
    1 contract for fire (SI 100,000)
    1 contract for storm (SI 100,000)
    (Total SI 200,000)

    So in the second cases the total exposure is double. However I think the total risk premium is the same....

    I must be missing something here so please help!
     
    NeedToQualify, Mar 12, 2008
    #1
  2. herewegoagain

    herewegoagain Member

    Motor - The exposure would double. At one time only one driver can drive the vehicle. So, one vehicle with two drivers should be contributing the same exposure as one driver and one vehicle.

    Number of drivers is a risk/rating factor, but shouldn't impact exposure.

    For household, I would have guessed that the "risk premium" should be the same. However, if pricing stochastically, simulations for two risks together may add the benefit of diversification between them, and hence come up with lower premium?
     
    herewegoagain, Mar 12, 2008
    #2
  3. shyguy

    shyguy Member

    missing the point

    If you remember the premium relates to the exposure then in the household example (assuming mutually exclusive nature of events and one property) the risk premium elements are additive but the exposure is not. Consider the construction of GLM risk premium models. For each peril, derive a risk premium and aggregate these




     
    shyguy, Mar 12, 2008
    #3
  4. NeedToQualify

    NeedToQualify Member

    Motor 1st case: I agree. The exposure is the same when we have 2 drivers. But this gives the same risk premium as the 2nd case. 2 drivers with 2 policies. Doesn't it?

    Houshold: I agree. Perils are additive. Again, this gives the same risk premium though as for the 2nd case...

    Intuitively this doesn't make sense to me....The exposure is double in the second cases so I would expect a double risk premium.

    As for stochastic pricing, yes this would take diversification into account. But diversification doesn't impact the risk premium. Only the capital and thus the profit requirement.
     
    NeedToQualify, Mar 13, 2008
    #4
  5. NeedToQualify

    NeedToQualify Member

    anyone? This is really puzzling me.
     
    NeedToQualify, Mar 27, 2008
    #5
  6. Ian Senator

    Ian Senator ActEd Tutor Staff Member

    I'm not quite sure what you're getting at here. Are you getting confused with risk premium and risk premium per unit of exposure perhaps?

    If you've got two identical policies with the same exposure, then they'll each pay the same risk premium.
     
    Ian Senator, Mar 28, 2008
    #6
  7. NeedToQualify

    NeedToQualify Member

    Basically, 2 perils on the same contract give the same premium amount as 2 contracts with 1 peril on each of them...However the max payout is double in the second case.
     
    NeedToQualify, Mar 28, 2008
    #7
  8. Ian Senator

    Ian Senator ActEd Tutor Staff Member

    Here's an example for household, assuming all perils equally likely, and independent:

    Scenario A
    One policy which covers theft and fire. Premium is £200.

    Scenario B
    Two policies.
    One covers theft only. Premium is £100.
    One covers fire only. Premium is £100.

    In scenario A, his house gets stolen(you know what I mean!), and later in the year it burns down too. 2 claims, both paid for.
    In scenario B, one gets stolen, the other burns down. 2 claims, both paid for.

    So..?
     
    Last edited: Mar 28, 2008
    Ian Senator, Mar 28, 2008
    #8
  9. NeedToQualify

    NeedToQualify Member

    The difference, to me, is that under scenario B the max payout is twice the max payout under scenario A. (The SI represents the max allowable payout in any year). I'm I wrong?
     
    NeedToQualify, Mar 28, 2008
    #9
  10. Ian Senator

    Ian Senator ActEd Tutor Staff Member

    Well, the SI could be, say, £1000 for fire and £1000 for theft. So you could claim up to £2000 max in both scenarios. This is assuming that the SI is the max for any one peril, not any one year (so you'd have to look at the policy wording to see what applies). In practice, with household, total losses are very rare indeed, so the SI is pretty arbitrary once it gets large enough (many companies offer 'unlimited' SI cover - more of a marketing gimmick really rather than a true exposure measure).
     
    Ian Senator, Mar 28, 2008
    #10

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