Solvency II  Solvency Capital Requirement Development (July, 2012)
Article Summary:
This article describes functionality in AXIS that can be used to model Solvency II solvency capital requirements (SCR). The features described in this article are designed to provide support for the standard formula as outlined by the European Insurance and Occupational Pensions Authority (EIOPA).
Background
Solvency II is a European Union (EU) regulatory project that provides an economic riskbased framework for the solvency supervision of insurance companies. The design of Solvency II relies on technical provisions which allow companies to meet their obligations to policyholders, and solvency capital requirements which should cover unexpected losses over a oneyear time horizon. Solvency II will apply to virtually all European Union insurers and reinsurers.
Pillars are defined by the EIOPA as a way of grouping Solvency II requirements. Pillar 1 covers all the quantitative requirements including Solvency Capital Requirement (SCR). SCR can be calculated using either a standard formula or, with regulatory approval, an internal model. Pillar 2 sets standards of risk management and governance within an insurance organization. Pillar 3 imposes greater levels of transparency for supervisors and the public.
This Knowledge Base article focuses on the Solvency Capital Requirement covered in Pillar 1.
Solvency II Calculations
In broad terms, Solvency II calculations can be broken down into 3 parts:
 Best estimate liability
 Risk margin
 Solvency capital requirement
Best Estimate Liability and Risk Margin
Solvency II requires insurance companies to set up technical provisions which corresponds to the current amount the insurance company would have to pay if it was to transfer its obligations immediately to a third party. The value of the technical provisions should be equal to the sum of a best estimate liability and a risk margin. Best estimate liability should equal the probability weighted average of future cash flows taking into account the time value of money.
Risk margin should correspond to the cost of providing an amount equal to the Solvency Capital Requirement (SCR) necessary to support the insurance obligations over the lifetime of the product. For the purpose of determining the Risk margin, SCR ignores avoidable market risk and the lossabsorbing capacity of deferred tax. The rate used in the determination of the cost of providing that amount is called the costofcapital rate. The costofcapital rate prescribed for Solvency II is 6%.
The technical provision can be determined in AXIS by using the Reserve method "Present value of cashflow plus cost of capital" in the liability modules. Note that this Reserve method is currently under beta feature code 473  "Cost of Capital Risk Margin", and the risk margin component of the calculation is not yet available in the Disability module. This reserve method allows users to project the Best estimate liability (Present value of cash flow) and Risk margin (Present value of cost of capital) at each reporting date in the Calendar year projection. By entering best estimate assumptions in the Reserve section and selecting one of the table methods that uses implied forward rates in the Interest rate table field, the user can run a Cell that projects the probability weighted cash flows and discounts them using the prevailing forward rates. Note that the “Reserve revaluation” switch must be set to "Based on Reserve Revaluation Frequency setting in dataset parameters".
Risk margin is determined by projecting future SCR using the best estimate assumptions and discounting the cost of providing the amount equal to the SCR necessary to support the insurance obligations over their lifetime. The parameters for the SCR calculation can be entered in the Solvency Capital Requirement composite table in the Required surplus section (see below). The SCR used to determine Risk margin ignores market risk (i.e. assumes all market risks are avoidable) and the adjustment for the risk absorbing effect of deferred tax. The costofcapital rate can be specified in the Reserve section and the calculated Risk margin and the associated SCR can be viewed using the Valuation Details category report.
Solvency Capital Requirement
SCR can be calculated using either a standard formula or, with regulatory approval, an internal model. Insurance companies can also deploy a partial model alongside the standard formula. SCR is intended to reflect all quantifiable risks that insurance companies might face, including:
 Counterparty risk,
 Life underwriting risk,
 Health underwriting risk,
 Nonlife underwriting risk,
 Market risk and
 Operational risk
SCR should correspond to the valueatrisk of the net assets of the insurer subject to a confidence level of 99.5% over a oneyear period assuming continued solvency. SCR should cover the risk of existing business as well as the new business expected to be written over the following 12 months.
Standard Formula
The standard formula is designed to be more risksensitive than the factorbased approach and categorizes risks into modules for capital purposes. The results are then aggregated, with diversification effects governed by a correlation matrix.
The projection of SCR using the standard formula can be activated by selecting the Solvency capital requirement composite table in the Required surplus section. Each row of this composite table (except Row 1) represents the modules listed above. The table in Row 1 allows users to estimate the diversification benefits on a policybypolicy basis. At the Higher level, users have the option to recalculate the diversification benefits on an aggregate basis using either a correlation matrix or a formula table.
Note that the "Reserve used for required capital" switch must refer to the Reserve used to calculate the Technical provision. The Risk margin calculation will automatically use this SCR’s parameters.
The tables in rows 2 – 7 are used to determine SCR for all modules and submodules:
Row 2  Counterparty Risk Module
This module reflects possible losses due to unexpected default or deterioration in the credit standing of the counterparties. SCR for counterparty (reinsurance) risk can be determined by specifying the default rates and recovery rates for each treaty or rating class. The Define switch in the table allows you to select the definition of loss given default (or reinsurance exposure).
Row 3  Life Underwriting Risk Module
This module covers the risk arising from the underwriting of life insurance policies. SCR for life underwriting risk can be determined by specifying shocks for various actuarial assumptions. For several submodules, the SCR is determined as the impact of the specified scenario on the net asset value, which is defined as the difference between assets and liabilities. To avoid circularity, the liabilities should not include risk margin within the calculations for the individual submodules.
For the mortality risk submodule, longevity risk submodule and lapse risk submodule, and disability risk submodule, users have the choice of specifying the assumption shocks either by policy year or by true financial year from reporting date.
Row 4 – Health Underwriting Risk Module
This module reflects the risk arising from health insurance. SCR for health underwriting can be determined by either specifying shocks for Other benefits or using a factorbased approach.
Row 5 – Nonlife underwriting risk module
This module reflects the risk arising from nonlife insurance obligations. SCR for nonlife underwriting can be determined by either specifying shocks for Other benefits or using a factorbased approach.
Row 6 – Market Risk Module
This module covers the risk arising from the level or volatility of market prices of financial instruments. Exposure is measured by impact of defined movements in the level of financial variables such as stock prices, interest rates and real estate prices. SCR for market risks can be estimated in liability Cells by using either a factorbased approach or by specifying shocks for the interest rates. In addition, at the Fund or Office level, SCR for market risks can also incorporate the exposures from invested assets at each reporting date of the Calendar year projection.
Row 7 – Operational Risk Module
This module reflects the risk of loss arising from inadequate or failed internal processes, or from personnel and systems, or from external events. SCR for operational risk can be determined using the factorbased approach.
The SCR for all modules and submodules can be viewed in the Solvency Capital Requirement category report. Note that the SCR in this category report represents the capital requirement for the company at each projected reporting date. The SCR in the Cost of Capital category report represents the capital used in the determination of the Risk margin at each recalculation date.
Internal Model
An internal model allows a much more tailored assessment of a particular business and its potential risks. Companies also have the option of a partial model, with some components of the standard formula replaced by results from an internal model. To use an internal model firms require prior supervisor agreement. To achieve approval, the insurer must demonstrate that the model passes a "use test", meets particular statistical quality standards, and is capable of being calibrated to the "one year 99.5%" level. The "use test" requires that the model is embedded within the system of risk management, is a key tool in decisionmaking processes, and is updated frequently to reflect the business’ risk profile. Even when approval is granted, companies must provide the supervisor with the standard formula SCR for 2 years.
AXIS already has a comprehensive set of tools for building the company’s internal model including the Stochastic Processing module. Please refer to Knowledge Base article 552 (linked below) for more information. For example, to determine the "one year 99.5%" capital requirement, you can set the "Years of projections" switch in the Block Projection Assumptions object to "Use 1 year" and select the appropriate setting in the "Liabilities after projection period" switch to calculate the terminal provision at the end of a one year horizon. The method and assumptions used to calculate the terminal provision can be entered in the corresponding reserve section at the Cell level. The calculated scenario results can also be ranked to calculate tail measures such as CTE or VaR. In the Annuity and Universal Life modules, users can set up stochastic on stochastic calculations by selecting "Scenario reserve" as the reserve method and "Use risk neutral scenarios in Asset Pricing Model" as the scenarios.
If you have questions on the SCR functionality and how AXIS can support your Solvency II modelling needs, please contact us through our website client portal (www.ggy.com/Client/).
Official Solvency II documents are available here.
