Complex Covers

Contract Definition Language (CDL) includes features to model complex covers.

These examples assume claims from one flood event affecting one location and causing (150k, 30k, 20k) USD loss to (Building, Contents, BI) unless stated otherwise.

Aggregate Limits and Attachments

Like terms, each individual amount in each cover can act cumulatively over time. The following example assumes a cover with both attachment and limit aggregate and three events in the contract period, similar to Aggregate Terms

Contract
 Declarations
  Currency is USD   
 Covers
  100% Share of 250k aggregate xs 250k aggregate
  1. In the first 200k event, the attachment is not met but is eroded down to 50k for subsequent events.
  2. In the second 200k event, the remaining 50k of attachment is used, and the layer pays 150k while eroding the limit for subsequent events to 100k.
  3. In the third 200k event, there is no effective attachment, and the remaining 100k of limit is used.

Cover Trees

Covers are not automatically put in order but can be explicitly constructed such that the payout of one becomes the subject of the other. When a contract does not have just one top-level cover, it pays the sum of its top-level covers (the ones no other Cover takes as their Subject).

Mechanically, in addition to being directly on the net of terms, a cover can be applied on another cover or the sum of a list of covers. A common use case for this is an occurrence layer capped by an aggregate limit.

Contract
 Declarations
  Currency is USD   
 Covers
  Occ: 100% Share of 125k xs 50k
  Agg: 100% Share of 200k aggregate ON occ

Event

Claim

Payout

1

200,000

125,000

2

200,000

75,000

3

200,000

0

Firstly, note Agg and Occ are just labels to identify the covers. No semantics come from the names themselves. Each event of 200k goes first through the Occ layer, then sends the result of that calculation (125k) through the Agg layer. The final contract payout is the sum of top-level covers (those covers on which there are no other covers) which in this example is the one cover, Agg. If there were any terms, the Occ cover would apply to the net of terms and then the Agg cover would apply to the output of the Occ cover.

Constrained Covers

Like terms, covers can also have subject constraints from a list of loss types, to a list of risks, by a list of causes.

The following example illustrates a per-risk location deductible and covers to sets of risks.

Contract
 Declarations
  Currency is USD   
 Covers
  Group1: 100% share of 300k xs 100k to R1, R2
  Group2: 100% share of 400k xs 100k to R3
 Deductibles
  25k per risk

Replicating the R1 claims (150k, 30k, 20k) to R2 and R3, the payout net of terms to Group1 of 350k and to Group2 of 175k produce layer payouts of 250k and 75k respectively. The contract pays 325k.

Payout Functions

Limit is the most common payout function for a cover. Given a net of attachment, the limit function is max(net of attachment,0). Other payout functions are sometimes used in practice and are supported in CDL. The following example illustrates another common payout function to pay a constant on the attachment being exceeded.

Contract
 Declarations
  Currency is USD   
 Covers
  100% share of Pay 300k xs 100k

Since the subject loss is 200k, the attachment is met and the cover pays 300k.

More complex payout functions can also be used, as required.

Contract
 Declarations
  Currency is USD   
 Covers
  100% share of Pay Max (1M - Subject, 0)

The contract pays 800k in this case, since max(1M-200k,0) = 800k.

Step Policies

Simple Step Policy

Taiwan earthquake policies are examples of simple step policies. If the claim is bigger than S1, pay P1, else pay 0.

Contract
 Declarations
  Currency is USD   
 Covers
  100% share of Pay 1M xs 150k

The 200k claim is bigger than 150k, so the contract pays 1M.

Medium-Complexity Step Policies

In Japan, step policies are written with multiple steps.

  1. If claim > S1, pay P1
  2. If S1 > claim > S2, pay P2
  3. And so on

CDL accomplishes this with payout covers per step, with different attachments, and a cover on those steps that pays the max of any step (so that the contract does not accidentally pay the sum of all steps).

The following example illustrates that, in addition to operating on the sum of a list of covers, a cover can be set to act on the max or min of a list of covers, or even on the diff of two covers.

Contract
 Declarations
  Currency is USD   
 Covers
  step1: 100% share of Pay 50k xs 75k
  step2: 100% share of Pay 150k xs 150k
  step3: 100% share of Pay 250k xs 225k
  final: 100% share on max(step1, step2, step3)

A subject loss of 200k will hit step2 and pay 150k. Step1 also pays its 50k. The final cover ensures that only the 150k is paid in the end.

Complex Step Policy

Steps might be for Building or Contents (but not the sum of Building and Contents). Sometimes step payouts are limited to the subject claim. See Expressions for more information about the mechanics used in this example.

Contract
 Declarations
  Currency is USD   
 Covers
  step1B: 100% share of Pay min (Subject, 50k) xs 75k for Building
  step1C: 100% share of Pay min (Subject, 50k) xs 75k for Contents
  step1: 100% share on Max(step1B, step1C)   
  step2B: 100% share of Pay min(Subject, 150k) xs 150k for Building
  step2C: 100% share of Pay min(Subject, 150k) xs 150k for Contents
  step2: 100% share on Max(step2B, step2C)   
  step3B: 100% share of Pay min(Subject, 250k) xs 225k for Building
  step3C: 100% share of Pay min(Subject, 250k) xs 225k for Contents
  step3: 100% share on Max(step3B, step3C)
  final: 100% share on max(step1, step2, step3)

Step1B pays 50k, and Step1C pays 0, so Step1 pays 50k all for Building. Step2 and Step3 pay 0 as the attachments are not met. Final pays 50k, all for Building.

Franchise Attachment

Like deductibles, attachments can be franchise. The covers limit acts on the cover’s entire subject if the subject > attachment, instead of its subject net of attachment.

Contract
 Declarations
  Currency is USD   
 Covers
  step1: 100% share of 300k xs 125k franchise

Since the 200k claim is larger than 125k, the full claim is eligible to be paid through the limit, and the contract pays 200k.