#StumpStumpo: Challenge RMS to model any re/insurance contract in RMS's Contract Definition Language

©2014 Risk Management Solutions, Inc. 1

#StumpStumpo – CDL Challenge Five Minutes into Exceedance 2014, RMS’s CEO Hemant Shah issued the Stump Stumpo challenge. Tweet a re/insurance contract with hashtag #StumpStumpo and Cody Stumpo, the Structure Language & CDL product manager, will see if it can be expressed in RMS’s Contract Definition Language. CDL has the benefit of making simple things simple, and complex things possible. In these cases, we are definitely focusing on the back half of that sentence. Here are the results, from both twitter and in-person challenges at Exceedance. If you want to try your hand at #StumpStumpo, tweet with that hashtag or just email [email protected].

1) Increasingly common in California Earthquake market, a Difference in Conditions policy where the entire account schedule erodes the attachment but only select locations are covered.

The solution uses the idea of covers taking other covers as their subject. A tree of covers can be formed in this way, and the contract pays the sum of top-level covers (those not the subject of some other cover).

• Make a sub schedule of everything but the covered locations (call it OtherLocs), and put a 10M limit on that

• Make a sub schedule of the covered locations (call it DIC) and pass that through unlimited

• Put the 10 xs 10 layer on top of the sum of those two. Covers C1: 100% Share of 10M to OtherLocs C2: 100% Share to DIC C3: 100% Share of 10M xs 10M on C1, C2 Let’s run some losses through to see it’s working how we expect. The contract has one top-level cover, C3, so C3 is also the contract payout.

Subject Loss 10M to otherlocs to DIC 10 x 10 on C1,

C2 OtherLocs DIC C1 C2 C3

0 5 0 5 0 0 10 0 10 0 0 15 0 15 5 0 20 0 20 10 5 0 5 0 0


5 5 5 5 0 5 10 5 10 5 5 15 5 15 10 5 20 5 20 10

10 0 10 0 0 10 5 10 5 5 10 10 10 10 10 10 15 10 15 10 10 20 10 20 10 15 0 10 0 0 15 5 10 5 5 15 10 10 10 10 15 15 10 15 10 15 20 10 20 10

2) One actually came in via twitter and could be answered in twitter’s 140-character limit

as well.

This solution uses the capability of a cover to have a payout function (in this case a constant) other than the usual limit.


The “Slope” cover pays the 1st 1M of loss. The “FlatLine” cover pays a flat negative 1M upon its 1M attachment being met. Those two covers work together to create the reverse franchise (pay the first 1M, but pay 0 for losses above 1M). The “Agg” cover is on the other two covers, meaning it takes their input as its subject. It then applies the 10M aggregate limit.

+

=

On each graph above, the horizontal axis is the Subject and the vertical axis is the Payout.

3) Another verbally delivered challenge – the assumed ceded swap. Two reinsurers want to effectively swap treaties. The standalone risk of the two treaties is similar even though they are exposed to different region / perils. Because of how the treaties correlate to the reinsurer’s portfolios, they each find the other’s treaty more attractive.

To model this, the challenge is not so much about CDL but the larger concept of Structure Language. While CDL is the heart of Structure Language, Position statements are the other small piece, but one that does a lot. The subject of each contract is a position, and the payout of each contract is a position. These payouts can be manipulated via simple operations (e.g. plus, minus, scale,…) to form other positions – which themselves can be the subject of other contracts or of reports. With this simple ability, it is easy to quickly create structures that model the cash flows and accounting needs of the industry. Structure Builder is an application that can depict a Structure graphically – it generates this picture based on the text of the Structure. The Blue positions are for Reinsurer1 and the Orange positions are for Reinsurer2. It should be noted that the arrows in the current version of Structure Builder depict dependency, not loss flow.


Structure RI1:Assumed is RI1:Cat1 + RI1:FromRI2 RI2:Assumed is RI2:Cat2 + RI2:FromRI1 RI1:Ceded is RI2:FromRI1 RI2:Ceded is RI1:FromRI2 RI1:Net is RI1:Assumed - RI1:Ceded RI2:Net is RI2:Assumed - RI2:Ceded Contract Declarations Name is RI1:Cat1 Subject is Cedant1 Description is {RI1's Treaty} Covers 100% Share of 25M xs 10M Contract Declarations Name is RI2:Cat2 Subject is Cedant2 Description is {RI2's Treaty} Covers 100% Share of 25M xs 20M Contract Declarations Name is RI2:FromRI1 Subject is RI1:Cat1 Description is {RI1 -> RI2} Covers 100% Share Contract Declarations Name is RI1:FromRI2 Subject is RI2:Cat2 Description is {RI2 -> RI1} Covers 100% Share


4) An emailed challenge – a contract with different layers by peril, an overall aggregate

limit, and a drop-down for the EQ layer. Well, this almost stumped me. Most of it follows straight off from the description, but the major question is how to get the drop to pay only under the proper circumstances, and how to get it to see the full subject in order to apply its layer. WSCover: 100% Share xs 240 by WS EQTop: 100% Share of 100 aggregate xs 270 by EQ EQDrop: 100% Share of 100 aggregate xs 220 on ?? EQOcc: 100% Share of 100 on EQTop, EQDrop Agg: 100% Share of 200 aggregate on Occ The EQOcc cover ensures that we do not double pay any losses between EQTop & EQDrop. The Agg cover puts an annual aggregate limit on losses from Wind, EQTop, & EQDrop. We want the subject of Drop to be all EQ losses after EQtop exhausts. Putting a cover on EQTop xs 100 Aggregate Franchise, and putting EQDrop on that, ensures that EQDrop will only see losses exactly when EQTop is exhausted. But we don’t want EQDrop at that point to see losses that have already been reduced by the xs 270 of EQTop. So we’ll make the payout of this intermediate cover be exactly what is not paid by EQTop. Covers WSCover: 100% Share of 100 xs 240 by WS EQTop: 100% Share of 100 Aggregate xs 270 by EQ Slider: 100% Share of Pay (EQTop.Subject – EQTop.Payout)

xs 100 Aggregate Franchise on EQTop EQDrop: 100% Share of 100 xs 220 on Slider EQOcc: 100% Share of 100 on EQTop, EQDrop Agg: 100% Share of 200 Aggregate on WSCover, EQOcc How does this work? The EQTop has a 100 Aggregate Limit, so stops paying after that. EQDrop is on Slider, which will make it see the full EQ loss minus the EQTop payout - but because it is xs the same 100 Aggregate that is the limit of EQTop, only once the EQTop Limit is exhausted. The EQOcc cover ensures that even in a very large event the EQ payout is only 100. A Contract’s payout is the sum of the payouts of its top level covers (those covers that are not the subject of some other cover). In this case, there is just one top level cover, Agg. So in the examples below, consider the payout of the Agg cover to be the payout of the contract.


Example 1) An Earthquake sequence arrives: 800, 300.

800 300 Subject Payout Subject Payout

WSCover 0 0 0 0 EQTop 800 100 300 0 Slider 100 700 0 300

EQDrop 700 100 300 80 EQOcc 200 100 80 80

Agg 100 100 80 80 Example 2) An earthquake sequence arrives 300, 800



EQDrop 0 0 730 100 EQOcc 30 30 170 100

Agg 30 30 100 100 Example 3) An earthquake sequence arrives 340, 300



EQDrop 0 0 270 50 EQOcc 70 70 80 80

Agg 70 70 80 80

5) Double place a layer with no protection underneath – this still legally counts as reinsurance since you cannot recover more than you lose.

The share of a cover is not limited to the 0-100% range, as there are many anticipated use cases where you might want something else.


Covers 200% Share of 50M xs 50M Indeed we can see that Payout < Subject for all possible claims of Subject and so it is reinsurance and not speculation.

6) Another verbally delivered challenge – a per risk with the smaller of a certain constant amount and each location’s Fire PML as the per risk limit. The per risk contracts are on an annual basis but have an interlocking clause.

An inelegant solution certainly exists – determine outside the product for each location what the effective risk limit is and make a cover in the treaty with that limit to the location. (Perhaps gather all those that have the same limits into per risk covers) Contract Declarations … Risk is Each Location Covers Pr225: 30% Share of 225M to HighValue per risk Pr150: 30% Share of 150M to Schedule150 per risk PR155: 30% Share of 155M to Schedule155 per risk … //many more covers potentially occ: 100% Share of 270M on PR225, PR150, PR155,… We can take advantage of the extensible data model to provide a more elegant solution. Any tenant will be able to add a field to the Location object. In this case add a field to your risk locations called e.g. FirePML and populate it at each Location with the Monetary Value of the Fire PML for that Location. CDL could then see that value and consume it in formulas. This makes the essence of the per risk contract a one-liner.


pr: 30% Share of min (225M, FirePML) per risk As per challenge #3 above, we will use Structure Language to properly model the interlocking clause. An interlocking clause across per risk treaties can be modeled as a contract whose subject is the treaties, and who applies a layer to that subject. The key is that position management allows this contract to take other treaties as its subject, and further - not have the intermediate contracts contribute to overall ceded or net.

Structure Construction_2014 is {Construction Book} / {Inception in 2014} Construction_2013 is {Construction Book} / {Inception in 2013} PerRisk is PR2013 + PR2014 Net is {Construction Book} - Interlocking

Contract Declarations Name is PR2013 Subject is Construction_2013 Inception is 1 Jan 2013 Expiration is 31 Jan 2013 Attachment Basis is Risk Attaching Covers pr: 30% Share of min (225M, FirePML) per risk occ: 100% Share of 270M on pr Contract Declarations Name is PR2014 Subject is Construction_2014 Inception is 1 Jan 2014 Expiration is 31 Jan 2014 Attachment Basis is Risk Attaching Covers pr: 30% Share of min (225M, FirePML) per risk occ: 100% Share of 270M on pr


Contract Declarations Name is Interlocking Subject is PerRisk Covers 100% Share of 270M

7) Another Structure Builder case. A cat treaty generates both payout (from reinsurer to

cedant) and reinstatement premium (from cedant to reinsurer). Cedant would like to see their net position net of reinstatement premium. Meanwhile, the reinsurer buys retro on the cat treaty payout only. They too would like to see their net net position.

For transparency’s sake in the diagram, I’ve simply modeled the reinstatement premium in it’s own contract.

Structure NetOfRIP is CatTTY - CatTTY.RIP Cedant:Net is Cedant:UNL - NetOfRIP Reinsurer:Net is NetOfRIP - Outward:Retro Contract Declarations Name is CatTTY Subject is Cedant:UNL Description is {Payout} Covers 100% Share of 10 xs 10 Contract Declarations Name is CatTTY.RIP Subject is Cedant:UNL Description is {ReinstPremium} Covers


10% Share of 10 xs 10 Aggregate Contract Declarations Name is Outward:Retro Subject is CatTTY Description is {Retro} Covers 100% Share of 3 xs 3

8) An anonymous challenge – each location has a deductible but the policy deductible in an event is just the largest deductible taken.

CDL anticipates exactly this case with its control over the interaction type of deductibles. Each deductible can have its own scope. In settling a claim, deductibles interact with deductibles of smaller scope and that interaction is controlled via the interaction function. The three interaction functions available currently are min, max, and single largest. Future developments will allow other interaction types such as controlling exactly which smaller-scoped deductibles contribute to the larger-scoped deductible (e.g. non-ranking deductibles, in-sequence deductibles). In the case of location deductibles vs. a policy deductible, the policy deductible has larger scope than any location deductible and so takes their output as part of its input. For all the examples, let’s imagine: Location Deductible Loss 1 100 500 2 200 150 3 300 0 So there are 250 of deductibles taken from the locations. Min(100, 500) + Min (200, 150) + Min (300, 0) = 250 A standard policy deductible of 300 would first apply to the Subject loss of (500 + 150) and say Min (300, 650) = 300. If the policy deductible is of interaction type min, it compares 300 to 250 and takes the larger (the deductible has to be at a minimum 300) as the effective deductible in this event. Deductibles 100 to Location1 200 to Location2 300 to Location3 300


Notice the policy deductible does not have any subject constraint – it’s scope is the contract subject. If the policy deductible is of interaction type max, it compares 300 to 250 and takes the smaller (the deductible can be at maximum 250) as the effective deductible in this event. Deductibles 100 to Location1 200 to Location2 300 to Location3 300 Max A Single Largest Deductible doesn’t have an amount. Nor for that matter does it have the ability to be standard or franchise or any other functional form. It simply selects the single largest deductible actually taken from amongst deductibles of smaller scope and uses that one going forward while refunding the rest. The effective deductible in this event would be 150. Deductibles 100 to Location1 200 to Location2 300 to Location3 Single Largest

#StumpStumpo: Challenge RMS to model any re/insurance contract in RMS's Contract Definition Language

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