1. ID informationeiopa.europa.eu/Publications/Other Documents/Instructions... · Web viewIn case...

Instructions regarding reporting templates for the

Non-Life underwriting risk Comparative Study (NLCS) on Internal Models (IMs)

Last update: 02/03/2018

General comments:

This document contains instructions that each selected solo undertaking participating in the NLCS is expected to follow when completing the questionnaire (put in an Excel workbook) related to this study.

For the purpose of these instructions:

- Scope:o Undertakings: Only selected solo undertakings with IMs comprising a non-

life underwriting risk module are considered.o Risks: All requested figures are understood to exclude catastrophe risks.

- Definition of undertaking: The term ‘undertaking’ means full IM undertaking, partial IM undertaking, and IM group in relation to solo results strictly.

- Time horizons:o ‘One-year time horizon’ is the basis on which the solvency capital

requirement (SCR) is calculated under article 101(3) of the Solvency 2 (S2) Directive.

o ‘Ultimate time horizon’ refers to the non-life model outputs that relate to risk over the time horizon of the run-off of the undertaking’s obligations to its policyholders, including obligations relating to business planned to be written in the 12 months following the reference date.

- Premium provisions: Premium provisions changes are to be treated as part of premium risk for this questionnaire unless stated differently.

- Currency and display: All monetary amounts are to be reported in EUR. If the original values are based on a foreign currency, please use the daily foreign exchange rate at the reference date as published by the ECB1 and convert it to EUR. Unless otherwise explicitly stated do NOT display monetary figures as multiples of EUR (like kEUR or MEUR) and NOT as percentages but as absolute amounts.

- Discounting: Where relevant, every amount should be discounted at the applicable risk-free rate. The market risk is out of scope of this study, i.e. the discount rates used should be deterministic and the ones prevailing at t=0. If another type of discount curve is used please provide explanations in the comments and describe your approach.

- Reinsurance: unless stated otherwise, all requested figures are gross of reinsurance.

- Quantiles: High quantiles represent adverse results for the undertakings: the underlying implicit distribution is indeed a loss distribution (i.e. claims - [some positive amounts]).

- Risk margin: No requested figure pertains to the risk margin.

1 https://www.ecb.europa.eu/stats/policy_and_exchange_rates/euro_reference_exchange_rates/html/index.en.html

Page 1 of 24

https://www.ecb.europa.eu/stats/policy_and_exchange_rates/euro_reference_exchange_rates/html/index.en.html

https://www.ecb.europa.eu/stats/policy_and_exchange_rates/euro_reference_exchange_rates/html/index.en.html

- Reconciliation: Where relevant, please make sure the given figures reconcile with the national IM QRTs. All the reported figures should also be consistent with the EIOPA QRTs S.17.01 and S.26.05.

- Unavailability of figures: In general it is expected that the requested figures in this questionnaire are available at at least one of the requested granularities (internal or Solvency 2 LoBs) and consistently reported to the extent possible (means add up, etc.). The figures should also be consistent with your national regulatory reporting. Any deviation from these assumptions should be explicitly mentioned and justified. If adjustments are needed, they should be described and justified in the relevant cells (e.g. comments). When no figure at all is available (even with adjustments), please let the related cells empty and provide the reasons of this unavailability in the comments cells.

For the sake of parsimony and readability, only the cells deemed not self-explanatory are further explained in this document with e.g. the intention and some necessary references. This document is intended to evolve over time to reflect the outcome of the Q&A process.

From the template “3.1 QUAL Prem risk - Int LoBs” onwards, the data requests only pertain to the following 4 S2 Lines of Business (LoBs):

- Motor vehicle liability;- Other motor;- General liability;- Fire and other damage to property.

Page 2 of 24

Template name Template description (high level)Overview Overview on the questionnaires content, logic and legend

1 ID informationEach submission should include this information in order to unambiguously identify the submitting undertaking and the submission date.

2 SegmentationsThe segmentations apply to all internal LoBs2 modelled for premium and reserve risks. It aims to understand the composition of internal LoBs and to map out their relation to the S2 LoBs.

3.1 QUAL Prem risk - Int LoBs

Qualitative questions on premium risk at the level of the internal LoBs.

These qualitative questions collect information on premium risk at the level of the internal LoBs to complement the quantitative questions.

They pertain to the internal LoBs mapped to the subset of S2 LoBs.

3.2 QUAL Res risk - Int LoBs

Qualitative questions on reserve risk at the level of the internal LoBs.

These qualitative questions collect information on reserve risk at the level of the internal LoBs to complement the quantitative questions.


3.3 QUANT Prem risk - Int LoBs

Quantitative questions on premium risk at the level of the internal LoBs.

These quantitative questions collect information on premium risk at the level of the internal LoBs to complement the qualitative questionnaire.


3.4 QUANT Prem risk - S2 LoBs

Quantitative questions on premium risk at the level of the S2 LoBs.

These quantitative questions collect information on premium risk at the level of the selected S2 LoBs in order to compare undertakings’ IMs’ outputs on a common basis.

3.5 QUANT Res risk - Int LoBs

Quantitative questions on reserve risk at the level of the internal LoBs.

These quantitative questions collect information on reserve risk at the level of the internal LoBs to complement the qualitative questionnaire.


3.6 QUANT Res risk - S2 LoBs

Quantitative questions on reserve risk at the level of the S2 LoBs.

These quantitative questions collect information on reserve risk at the level of the S2 LoBs in order to compare

2 A definition of internal LoB is given in the section dedicated to the Segmentations template.

Page 3 of 24

undertakings’ IMs’ outputs on a common basis.

4. Comments

The undertaking’s comments related to the completion of the above templates.In the first column the undertaking should select from the drop-down list the template name to which the comment in question relates and enter their comment.

Comments are especially needed if simplifications were necessary to arrive at some results, to avoid misinterpretations, etc.

Each participating undertaking is expected to submit all of the above templates completed in accordance with the outputs available from its IM. If the undertaking is not able to submit a template partly or in full, it should provide explanations in the “4. Comments” template.

For each template the undertaking should enter the information required in each green-shaded cell, select information required from a drop-down list in each blue-shaded cell, and make no amendments to any other (protected) cell in the template.

Instructions:

The instructions for each of the above templates are set out in the following tables. The column ‘ITEM’ identifies the item to be reported by reference to the columns and rows (if applicable) as shown in the template.

Page 4 of 24

Table of Contents

1. ID INFORMATION............................................................................6

2. SEGMENTATIONS...........................................................................7

3.1 QUAL PREM RISK - INT LOBS...................................................9

3.2 QUAL RES RISK - INT LOBS....................................................11

3.3 QUANT PREM RISK - INT LOBS.............................................13

3.4 QUANT PREM RISK - S2 LOBS...............................................15

3.5 QUANT RES RISK - INT LOBS.................................................16

3.6 QUANT RES RISK - S2 LOBS...................................................20

4. COMMENTS.....................................................................................21

5. APPENDIX – NOTATIONS AND RISKS’ BREAKDOWN FOR PREMIUM & RESERVE RISKS....................................................22

1.1.1. Solvency Capital Requirement and Net Asset Value. . .221.1.2. Stylized Solvency 2 balance sheets....................................22

Page 5 of 24

1. ID informationGeneral comments:

This section relates to the identification of each undertaking.

ITEM INSTRUCTIONS

ID01 Undertaking name

Legal name of the undertaking. Needs to be consistent over different submissions.This should be the same as the undertaking name reported in Solvency2 reporting template S.01.02.01.

ID02Undertaking identification code (preferably Legal Entity Identifier – LEI)

This should be the same as the undertaking identification code reported in Solvency 2 reporting template S.01.02.01

ID04 Reporting submission date Expected format: DD/MM/YYYY.

Page 6 of 24

2. SegmentationsGeneral comments:

This section relates to the segmentations used to model the premium and reserve risks for all internal LoBs.

An internal LoB should be understood as the calibration granularity level, the level at which the parametrization of the risks is performed.

Information on what every internal LoB contains should be given. Furthermore the internal LoBs should be mapped to the S2 ones and necessary adjustments mentioned. S2 LoBs in the drop-down list refer to the non-life LoBs as defined in the Annex I of the Solvency 2 delegated regulation (the so-called level 2).

The list of internal LoBs should be complete in contrast to the other templates which focus on a subset of S2 LoBs.

This mapping between internal and Solvency 2 LoBs is requested for all internal LoBs in order to check the materiality of the Solvency 2 LoBs left out of this edition of the study and to pave the way towards a more comprehensive analysis of the aggregation.

As mentioned in the introductory comments, premium provisions changes are to be treated as part of premium risk for this questionnaire unless stated differently. This remark applies in particular to the segmentations template: no dedicated premium provisions risk module appears in this template. In case the risk of changes in premium provisions is modelled separately from premium risk, the internal LoBs concerned should be reported with the prefix “Premium_Provisions_LoB_(NLCS)” in the premium risk table.

For the sake of parsimony and readability, below are listed the items pertaining to both premium and reserve risks simply separated by a slash (‘/’).

ITEM INSTRUCTIONS

C01 / 06

Premium / Reserve risk –

Internal LoBName of the internal LoB

This column lists the names of all internal LoBs that are used to calculate the premium / reserve risk.

C02 / 07 Premium / Reserve risk –

Description of the internal LoBPlease be as descriptive as possible so it is clear what the LoB entered contains. For example, include whether

Premium risk: In case the risk of changes in premium provisions is modelled separately from premium risk, please report that internal LoB with the prefix “Premium_Provisions_LoB_(NLCS)”.

If applicable, these prefixed internal LoBs will then be filled in in the premium risk-related templates where it makes sense to do so.

Premium / Reserve risk: The description of each internal LoB should include the distribution channel as well as any information which was

Page 7 of 24

the business is personal or commercial, its selling channel and where it is located.

relevant for the chosen segmentation.You can also mention these information in the relevant comment cells.

C03 / 08


Closest Solvency 2 LoB chosenChoose from the drop-down list

Please select the S2 LoB that best fits into each internal LoB.

C04 / 09


Description of any adjustments performed to go from the internal LoB to the S2 one (especially on the SCR)

If the S2 LoB is composed of more than one internal LoB or an internal LoB has to be decomposed in order to be represented in several S2 LoBs, please explain the methods used, especially how the SCR at S2 LoB level was derived from the SCR at the internal LoB level.

C05 / 10


Expected earned gross premiums over the 12 months after the reference date / Gross BE of outstanding claims as at the reference date

Measure (weight) to estimate the importance of each internal LoB.

Gross BE of outstanding claims should be understood as including IBNR.

Page 8 of 24

3.1 QUAL Prem risk - Int LoBsGeneral comments:

This template should be filled in before the template “3.3 QUANT Prem risk - Int LoBs” as the internal LoB selection of the former will populate the later.

With respect to these internal LoBs, the questions below concerning premium risk should be answered.

Questions related to the prefixed premium risk internal LoBs (“Premium_Provision_LoB_(NLCS)”) may be filled in where needed and where it makes sense to do so.

In order to facilitate the work of supervisors in charge of analyzing and interpreting your answers to these qualitative questions, please use as much as possible the notations of regulatory texts on Solvency 2.For the same reasons, regarding the definition of premium risk and its related SCR, please use the notations defined in appendix and refer to the exposed risks’ breakdown thereof as much as possible when explaining your approach.

ITEM INSTRUCTIONS

QUALPRER0101QUALPRER0102

Risk profileCountry- and undertaking-specific (from the same country) features

If your undertaking belongs to a group, your group may have this knowledge and you are free to discuss this topic within your group. The ultimate responsibility lies however with you.One aim of this study is to learn about the self-awareness of undertakings with respect to other markets.

QUALPRER0103

Risk profileWhat is the main type of business written?Please explain if "Other" was chosen.

Entries in the drop-down list:- Retail- Commercial- Industrial- Other

Undertakings have to choose one among the possible choices: (generally speaking “main” means the business with the highest premiums).

QUALPRER0201

Consistency between the IM and the Solvency 2 balance sheetPlease explain how the consistency requirement between premium risk and the Solvency 2 balance sheet has been implemented.

The consistency requirement can be found in article 121 of the Directive.

Page 9 of 24

QUALPRER0301

Risk and SCR definitionPlease give the definition chosen for premium risk and its SCR.

Please use the notations defined in appendix and refer to the exposed risks’ breakdown thereof as much as possible when explaining your approach.

QUALPRER0402 Odd column

Risk horizon

If premium risk is modelled on an ultimate view first, what method is used to arrive at the one-year view?Please explain if "Other" was chosen.Please provide a brief explanation of the method used. (How is the emergence pattern computed? On what is the emergence pattern applied?) and the reason this modelling approach was chosen.

For emergence pattern it is intended a methodology used to get the one year view from the ultimate view. Please add all comments and description needed about the method used.

Page 10 of 24

3.2 QUAL Res risk - Int LoBsGeneral comments:

This template should be filled in before the template “3.5 QUANT Res risk - Int LoBs” as the internal LoB selection of the former will populate the later.

With respect to these internal LoBs, the questions below concerning reserve risk should be answered.

In order to facilitate the work of supervisors in charge of analyzing and interpreting your answers to these qualitative questions, please use as much as possible the notations of regulatory texts on Solvency 2.For the same reasons, regarding the definition of reserve risk and its related SCR, please use the notations defined in appendix and refer to the exposed risks’ breakdown thereof as much as possible when explaining your approach.

CELL IDENTIFIER

ITEM INSTRUCTIONS

QUALRESR0101QUALRESR0102

Risk profileCountry- and undertaking-specific (from the same country) features

If your undertaking belongs to a group, your group may have this knowledge and you are free to discuss this topic within your group. The ultimate responsibility lies however with you.One aim of this study is to learn about the self-awareness of undertakings with respect to other markets.

QUALRESR0103

Odd column

Risk profile

What is the main type of business you have been underwriting?Please explain if "Other" was chosen.

Entries in the drop-down list:- Retail- Commercial- Industrial- Other

Undertakings have to choose one among the possible choices: (generally speaking “main” means the business with the highest reserves).

QUALRESR0301

Odd column

Consistency between the IM and the Solvency 2 balance sheet

Please explain how the consistency requirement between reserve risk and the Solvency 2 balance sheet has been implemented.

The consistency requirement can be found in article 121 of the Directive.

Page 11 of 24

QUALPRER0201

Risk and SCR definitionPlease give the definition chosen for reserve risk and its SCR.

Please use the notations defined in appendix and refer to the exposed risks’ breakdown thereof as much as possible when explaining your approach.

QUALRESR0302

Odd column

Risk HorizonIf reserve risk is modelled on an ultimate view first, what method is used to arrive at the one-year view?Please explain if "Other" was chosen.Please provide a brief explanation of the method used. (How is the emergence pattern computed? On what is the emergence pattern applied?) and the reason this modelling approach was chosen.

For emergence pattern it is intended a methodology used to get the one year view from the ultimate view. Please add all comments and description needed about the method used.

QUALRESR0701

Odd column

Computations of volatilities

If an ultimate view is modelled first, what methodology is used to model it?Please provide a brief description of the approach and explain if "Other" was chosen.

Entries in the drop-down list:- Closed-formula approach (e.g. Mack)- Simulation-based approach (e.g.

“bootstrap” variants)- Internal benchmark (e.g. parameters from

an internal LoBs are used on another internal LoB)

- External benchmark (e.g. parameters from an external source are used on an internal LoB)

- Other

QUALRESR0901

ReinsuranceHow do you take into account the risk mitigation effects of reinsurance for this internal LoB?

To our knowledge the reinsurance effects in reserve risk are usually modelled in a much less granular way than in premium risk (e.g. gross-to-net ratio).Please describe your approach in the free-text cell.

Page 12 of 24

3.3 QUANT Prem risk - Int LoBsGeneral comments:

This template should be filled in after the template “3.1 QUAL Prem risk - Int LoBs” as the internal LoB selection of the later will populate the former.

With respect to these internal LoBs, the questions below concerning premium risk should be answered.

Prefixed internal LoBs (“Premium_Provision_LoB_(NLCS)”) may be filled in where needed and where it makes sense to do so.

As mentioned in the introductory comments, here are definitions related to both time horizons:

- ‘One-year time horizon’ is the basis on which the solvency capital requirement (SCR) is calculated under article 101(3) of the Solvency 2 Directive.

- ‘Ultimate time horizon’ refers to the non-life model outputs that relate to risk over the time horizon of the run-off of the undertaking’s obligations to its policyholders, including obligations relating to business planned to be written in the 12 months following the reference date.

Regarding parameter uncertainty the following definition3 was chosen: the prediction uncertainty (or error) – of e.g. the claim development result in reserve risk – is generally split into a process error and an estimation error, the latter being also called parameter uncertainty or parameter error. Parameter uncertainty is the possibility that the parameters used to define the model are incorrect given that the model is correct. This possibility occurs, firstly, because there is only a (sometimes very) limited amount of data to estimate the parameters. Secondly, the parameters themselves will evolve through time, so those applicable for future events are always unknown at the present.

If a CAT risk is included in the LoB Fire (for example Windstorms), it is not required to make an artificial run to exclude it. This specificity should however be mentioned in the comments cells.

ITEM INSTRUCTIONS

PRERG201

OddorEven column

Gross premium risk data

One-yearorUltimate

Mean of claims and expenses

See general comments on time horizons.

The “mean of claims and expenses” is the sum of mean of claim and mean of expenses.

3 For references, see for instance:Cairns (A. J. G.) (2000) A Discussion of Parameter and Model Uncertainty in InsuranceWalker (S.) (1996) Workshop on Stochastic Error, Parameter Error & Model Error

Page 13 of 24

PRERG301 to 306

Oddoreven column


One-yearorUltimate

0.1%, 0.5%, 5%, 95%, 99.5%, 99.9% percentiles of premium risk


PRERG401 to 403

Oddoreven column


One-yearorUltimate

Effects of parameter uncertainty (if applicable and available)


If your final SCR figures include parameter uncertainty, then please give here figures without parameter uncertainty.Vice-versa, if your final SCR figures don't include parameter uncertainty, then please give here figures with parameter uncertainty.

If not available, please let the cell empty.

Page 14 of 24

3.4 QUANT Prem risk - S2 LoBsGeneral comments:

Prefixed internal LoBs (“Premium_Provision_LoB_(NLCS)”) must be included.

Individual cell references of this template are the same as the ones mentioned in the section “3.3 QUANT Prem risk - Int LoBs”.

The only additional cell in this template is the one below:

CELL IDENTIFIER

ITEM INSTRUCTIONS

PRERG104

Odd and even columns(merged cells)


Volume measure of the premium risk in the Standard Formula

Please insert the volume measure asked at SF level.

Page 15 of 24

3.5 QUANT Res risk - Int LoBsGeneral comments:

This template should be filled in after the template “3.2 QUAL Res risk - Int LoBs” as the internal LoB selection of the later will populate the former.

As mentioned in the introductory comments, here are definitions related to both time horizons:

- ‘One-year time horizon’ is the basis on which the solvency capital requirement (SCR) is calculated under article 101(3) of the Solvency 2 Directive.

- ‘Ultimate time horizon’ refers to the non-life model outputs that relate to risk over the time horizon of the run-off of the undertaking’s obligations to its policyholders, including obligations relating to business planned to be written in the 12 months following the reference date.

Regarding parameter uncertainty the following definition4 was chosen: the prediction uncertainty (or error) – of e.g. the claim development result in reserve risk – is generally split into a process error and an estimation error, the latter being also called parameter uncertainty or parameter error. Parameter uncertainty is the possibility that the parameters used to define the model are incorrect given that the model is correct. This possibility occurs, firstly, because there is only a (sometimes very) limited amount of data to estimate the parameters. Secondly, the parameters themselves will evolve through time, so those applicable for future events are always unknown at the present.

ITEM INSTRUCTIONS

RESR002


Data-history

Number of calendar years used to calibrate attritional claims

What is looked for here is the data history and not the development of claims. Some accident years may have incomplete developments.

RESRG101


Gross reserve risk data

Claims provisions derived from the IM before any Solvency 2 balance sheet reconciliation adjustments

Claims provisions as of the reference date and derived from the internal model. Give this value before any adjustment (e.g. scaling for consistency reasons).

In case there is no difference to the standard formula claim provisions, please explain the rationale and approach.

RESRG102

Odd and even columns


Provisions as of the reference date

4 For references, see for instance:Cairns (A. J. G.) (2000) A Discussion of Parameter and Model Uncertainty in InsuranceWalker (S.) (1996) Workshop on Stochastic Error, Parameter Error & Model Error

Page 16 of 24

(merged cells)BE of claims provisions

RESRG201 to 206

Oddoreven column


One-yearorUltimate

0.1%, 0.5%, 5%, 95%, 99.5%, 99.9% percentiles of reserve risk


RESRG301

Oddoreven column


One-yearorUltimateEffects of parameter uncertainty (if applicable and available)

Standard deviation of reserve risk without parameter uncertainty


Figure to be provided on a best-effort basis.

Please give results without parameter uncertainty. If the results had to be acquired via approximations, please describe them in the comments template.


RESRG302

Oddoreven column


One-yearorUltimateEffects of parameter uncertainty (if applicable and available)

99.5% percentile of reserve risk without parameter uncertainty





RESRG303

Oddoreven column


One-yearorUltimateEffects of parameter uncertainty (if





Page 17 of 24

applicable and available)

SCR of reserve risk without parameter uncertainty

RESRN101

Odd column

Net reserve risk data

Claims provisions derived from the IM before any Solvency 2 balance sheet reconciliation adjustments

Claims provisions as of the reference date and derived from the internal model. Give this value before any adjustment (e.g. scaling for consistency reasons).

In case there is no difference to the standard formula claim provisions, please explain the rationale and approach.

RESRN102

Odd column


BE of claims provisions

Best Estimate as of the reference date.

RESRN201 to 206

Oddoreven column


One-yearorUltimate0.1%, 0.5%, 5%, 95%, 99.5%, 99.9% percentiles of reserve risk


RESRN207

Oddoreven column


One-yearorUltimateMean of reserve risk

See general comments on time horizons.Figure to be provided on a best-effort basis only if readily available.

RESRN208

Oddoreven column


One-yearorUltimateStandard deviation of reserve risk


RESRN209

Oddoreven column


One-yearorUltimateSCR of reserve risk


Page 18 of 24

Page 19 of 24

3.6 QUANT Res risk - S2 LoBsGeneral comments:

Individual cell references of this template are the same as the ones mentioned in the section “3.5 QUANT Res risk - Int LoBs”.

The only additional cell in this template is the one below:

CELL IDENTIFIER

ITEM INSTRUCTIONS

RESRG102Odd and even columns(merged cells)


Volume measure of the premium risk in the Standard Formula

Please insert the volume measure asked at SF level.

Page 20 of 24

4. CommentsGeneral comments:

This section relates to any additional comment which might be necessary to contextualize the information provided in any of the previous sections. This includes e.g. clarifications, suggestions for future versions of this template, etc.

Please add lines as appropriate.

CELL IDENTIFIER

ITEM INSTRUCTIONS

C01 Tab name Options:- Overview- 1.0 ID information- 2.0 Segmentations- 3.1 QUAL Prem risk - Int LoBs- 3.2 QUAL Res risk - Int LoBs- 3.3 QUANT Prem risk - Int LoBs- 3.4 QUANT Prem risk - S2 LoBs- 3.5 QUANT Res risk - Int LoBs- 3.6 QUANT Res risk - S2 LoBs

C02 Row reference Row reference to be used may be found in red coloured cells (e.g. R001 in Template “2.0 Segmentations”)

If an entire row is affected please leave the column reference empty.

C03 Column referenceIf applicable

Column reference to be used may be found in red coloured cells (e.g. C01 in Template “2.0 Segmentations”)

If an entire column is affected please leave row reference empty.

C04 Comment number for row and column referenceIn case of several comments related to one cell

C05 Comment Description of issue.

Please keep your explanation short.

Page 21 of 24

5. Appendix – Notations and risks’ breakdown for premium & reserve risksThe intention of this appendix is to provide undertakings with common notations and risks’ breakdowns for premium and reserve risks.The expected benefits of providing such a common risk ‘alphabet’ are twofold: 1) to help undertakings to understand what is expected in the qualitative questions on “Risk and SCR definition” and give them a ‘reference’ point to answer these questions and 2) to help supervisors with the analysis of the answers to these questions.

The aim of this appendix is to define common notations as well as “theoretical” ( i.e. pure Solvency 2-compliant) premium and reserve risks derived from an annual variation of basic own funds computed on a Solvency 2 balance sheet, as specified in the Directive (e.g. article 101).

To that purpose a basic definition of the general SCR (i.e. regardless of the underlying risk) is first given and then two simplistic5 Solvency 2 balance sheets seen at two different dates separated by one year from each other, namely year N and year N + 1, are set up in order to look more closely at the sole non-life underwriting risk SCR.

1.1.1. Solvency Capital Requirement and Net Asset ValueThe Solvency 2 Directive defines the SCR as the amount to which the basic own funds at the end of year N could be reduced6 so as to ensure that the probability of economic insolvency in a one-year time equals 0.5%. Economic insolvency in a one-year time is defined as the point in time where the net asset value (NAV or basic own funds) at the end of year N + 1 becomes negative, i.e. formally7:

SCR = NAV (N ) such as P [NAV (N+1 )<0 ]=P [NAV (N )+∆NAV<0 ]=0.5 %

where NAV (N+1 )−NAV (N )=∆NAV .

It then comes that SCR=−q0.5% (∆NAV )=q99.5 % (−∆NAV ) .

1.1.2. Stylized Solvency 2 balance sheetsBelow is a simplistic Solvency 2 balance sheet of an undertaking only subject to the non-life underwriting risk between two consecutive years from which the ∆NAV will be computed:

5 In particular the financial / investment income is neglected.

6 In other terms, it means that the SCR at the end of year N is the amount of NAV (N ) which saturates the inequality

P [NAV (N )+∆NAV<0 ]≥0.5 %.

7 To be fully accurate, a discount factor should be added, i.e. the random variable that we look at should be NAV (N )+δ×∆NAV , with δ the discount factor between the end of year N and the end of year N + 1. Nevertheless, for the sake of simplicity and readability, this factor will be simply omitted here.

Page 22 of 24

N N + 1Assets NAV(N) Assets NAV(N + 1)

Economic value of non-life liabilities(N)

+ Written premiums(N + 1)Economic value of non-life liabilities (N + 1)- Claims settlements(N + 1)

- Expenses(N + 1)

It then comes:

∆NAV=Written premiums (N+1 )−Claims settlements (N+1 )−Expenses (N+1)

+Economic value of non-life liabilities(N ) – Economic value of non-life liabilities(N+1) .

Article 77 of the Directive defines the economic value of liabilities as “The value of technical provisions shall be equal to the sum of a best estimate and a risk margin […]”.

In particular for the non-life underwriting risk:

Economic value of non-life liabilities (N )=BEPCO (N )+BEPremium provisions (N )+RiskMargin (N )

where BE stands for Best Estimate and PCO for Provisions for Claims Outstanding.

The claims settled during the year N + 1 are then split according to their accident years, i.e. between claims occurred until the end of year N (index ‘→N ’) and those occurred only in year N + 1 (index ‘N+1’):

Claims settlements (N+1 )=Claims settlements→N (N+1 )+Claims settlementsN+1 (N+1 ) .

The same split is performed and the same notations adopted for the Best Estimate of PCO computed at the end of year N + 1:

BEPCO (N+1 )=BEPCO→N (N+1)+BEPCO

N+1(N+1) .

It finally comes:

∆NAV

¿ Written premiums (N+1 )−Claims settlements (N+1 )−Expenses (N+1 )+BEPremium provisions (N )−BEPremium provisions (N+1 )+BEPCO (N )−BEPCO (N+1 )+RiskMargin (N )−RiskMargin (N+1 )

¿BEPremium provisions (N )+Written premiums (N+1 )−BEPremium provisions (N+1 )−Claims settlementsN+1 (N+1 )−BEPCON +1 (N+1 )−Expenses (N+1 )

+BEPCO (N )−(Claims settlements→N (N+1 )+BEPCO→N (N+1 ) )

+RiskMargin (N )−RiskMargin (N+1 )

= Technical result of the new accident year+Claims development result due to former accident years +Risk margin variation.

Article 13 (30) of the Directive defines the non-life underwriting risks as “the risk of loss or of adverse change in the value of insurance liabilities, due to inadequate pricing and provisioning assumptions”.

Page 23 of 24

A premium (or pricing) risk can then be defined as the adverse (i.e. negative) evolution over one year of the following random variable:

A “theoretical” metric of the premium risk

Technical result of the new accident year =BEPremium provisions (N )+Written premiums (N+1 )−BEPremium provisions (N+1 )−Claims settlementsN+1 (N+1 )−BEPCO

N+1 (N+1 )−Expenses (N+1 ) .

Note that the random quantity Claims settlementsN+1 (N+1 )+BEPCON+1 (N+1 ) may be

modelled as a whole (e.g. as the ultimate estimate cost of the claims occurred during the accident year N + 1).

As for the reserve risk, it can be defined as the adverse (i.e. negative) evolution over one year of the following random variable:

A “theoretical” metric of the reserve risk

Claims development result due to former accident years =BEPCO (N )−(Claims settlements→N (N+1 )+BEPCO

→N (N+1 ) ) .

As a side and final remark, the random variable of the ultimate counterpart of the (one-year) reserve risk defined above can be written:

Ultimate reserve risk “random variable” = ∑i ≥1

Claims settlements→N (N+i ) .

Page 24 of 24

Date post:	30-May-2018
Category:	Documents
Upload:	doduong
View:	213 times
Download:	0 times