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Variance of deferred annuity benefit

Discussion in 'CT5' started by r_v.s, Apr 12, 2014.

  1. r_v.s

    r_v.s Ton up Member

    Would the variance of benefit of a continuous deferred whole life annuity be the same as an annuity a normal whole life annuity? Or would it reduce because of the probability of death during the deferment period?

    For instance if EPV = v^2*2p63* a65 (continuous annuity) :)o i dont know how to put the bar on a!). Would the var be v^4* (2p63)^2 * var of annuity benefit as usual?
     
    r_v.s, Apr 12, 2014
    #1
  2. John Potter

    John Potter ActEd Tutor Staff Member

    Coming up with a variance formula for this would be extremely difficult because

    PV = {annuity for T63 years if T63>2
    or {0 if T63<2

    If this came up in the exam, I would certainly be giving it a miss - your formula below is almost certainly wrong, you can't just square probabilities like this. I know we square constants when they come outside the variance but probabilities can't come outside the variance because they're part of working it out!

    I don't even think we could reasonably say whether the variance compared to a whole life annutiy for a 63-year old goes up or goes down. It's not obvious to me anyway. Probably up if you think that we are simply swapping all the possible annuities they would have got if T63<2 with the number 0, (which is further from the mean). However, don't take my word for this, I may be wrong!

    John
     
    John Potter, Apr 14, 2014
    #2
  3. T.Z

    T.Z Member

    How about the variance of payment paid only temporarily for a term of say,10 years and one paid annually in advance?
     
    T.Z, Apr 20, 2020
    #3

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