VoseAggregateTranche

See also: VoseAggregateMC

=VoseAggregateTranche(Frequency, SeverityDistributionObjectObject, {TrancheMinima}, TrancheMaxima})

 

 

Example model

Insurance companies often share the exposure they take on in providing insurance cover by splitting the coverage into tranches. For example, in the following graph insurance is being provided against a possible damage that is estimated to follow a Lognormal distribution with a mean of $6000 and standard deviation of $7000. There is a deductible of $3000 which means that the insured party pays the first $3000 of any damage. There are three other tranches of cover:

  1. 3000 - 8000

  2. 8000 - 15000

  3. >15000

VoseAggregateTranche is an array function with length equal to the number of tranches defined within the function. It returns random samples of the total amount that would be paid out in each tranche.

Let there be T tranches. Then the function applies the following logic:

Sample from the frequency distribution (let k be the sampled value, an integer);

 For i = 1 to k:

Take random sample from severity distribution (let S(i) be its value)

    For t = 1 to T:

SUM(t) = SUM(t) + IF(S(i)> Min(t), MIN(S(i) – Min(t), Max(t) – Min(t)),0)

    Next t

 Next i

End

The result is an array of values SUM(1)…SUM(T) containing the payouts for each tranche. Note that ”r+infinity” is an allowed input for a maximum value of a tranche.

The main additional value provided by VoseAggregateTranche is that the correlation between exposures in each tranche is retained. Thus, as in the example model, an insurer can correctly gauge the exposure of covering more than one tranche, or fractions of several tranches.

 

Note:  It is not required that the {Min} and {Max} arrays are non-overlapping, but the user should use caution in this situation since summing any of the overlapping parts of the output array will double count the exposure.

It is also not required that the {Min} and {Max} arrays cover the entire domain of the severity distribution. For example, an insurer may only be interested in two non-contiguous tranches it proposes to cover. However, the sum of the output array will then no longer be the aggregate exposure to all insurers.

 

 

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