The International ERM Glossary is intended to provide users with a set of definitions that are in common usage around the world by actuaries, regulators and members of the insurance industry. The purpose in developing the glossary is to help provide a common understanding of the terms currently in use, as definitions and meanings have varied over time, and among practitioners. It can also be used as a training and educational tool for regulators.

The glossary can be consulted per letter, organization or grouping.

**DISCLAIMER:** The content of the International ERM Glossary has been compiled by the Joint ORSA Subcommittee of the Insurance Regulation Committee and the Enterprise and Financial Risk Committee of the IAA. This information has been collated and presented for educational and informational purposes to the members of the IAA and interested parties. The IAA assumes no responsibility for the accuracy, completeness, currency, reliability of the information in the International ERM Glossary or access to any information contained on any of the sources cited in the Glossary. The IAA, its employees and officers shall not be liable for any loss or damage, direct or indirect, which may arise or occur as a result of the use of or reliance upon any of the material in the International ERM Glossary.

Term | Grouping | Organization or Jurisdiction Defining Term | Source of Definition | Definition |
---|---|---|---|---|

Conditional Tail Expectation or Tail VaR (Tail Value at Risk) | Methods | IAIS | IAIS Supervisory Material | Value at Risk (VaR) plus the average excess over the VaR if such excess occurs over a specified amount of time. |

Conditional Tail Expectation or Tail VaR (Tail Value at Risk) | Methods | International Actuarial Association | IAA - Acturial Aspects of ERM for Insurance Companies | Conditional Tail Expectation or "CTE" or Tail Value at Risk ("TVaR") is the mean of the distribution above a certain percentile or confidence level (a) or in other words, the expected value of a loss given that the loss is above a specified threshold, which is defined according to a specified percentile value a. This risk measure has many other names including Tail Value at Risk, Tail Conditional Expectation and Expected Shortfall. |

Conditional Tail Expectation or Tail VaR (Tail Value at Risk) | Methods | International Risk Management Institute | IRMI Terms | An economic cost of ruin (ECOR)-like measure in the sense that both the probability and the cost of "tail events" are considered; the calculation differs from ECOR in such a way that it has a desirable statistical property (i.e., coherence). |

Conditional Tail Expectation or Tail VaR (Tail Value at Risk) | Methods | The European Economic Area | CEA Solvency II | A coherent risk measure. For a given confidence level 1-a it measures the average losses over the defined threshold (typically set as the VaR for a given quantile), i.e. the conditioned mean value, given that the loss exceeds the 1-a percentile. |

Conditional Tail Expectation or Tail VaR (Tail Value at Risk) | Methods | United States | NAIC ORSA MANUAL | A measure of the amount of risk that exists in the tail of a distribution of outcomes, expressed as the probability weighted average of the outcomes beyond a chosen point in the distribution. |

Correlation Matrix | Methods | The European Economic Area | Solvency II | Not specifically defined. The correlation coefficients for the aggregation of the risk modules, as well as the calibration of the capital requirements for each risk module, shall result in an overall Solvency Capital Requirement.(Solvency II Directive art. 104.3) |

Correlation Matrix | Methods | United States | NAIC ORSA MANUAL | A symmetric matrix specifying pairwise interactions between a set of variables or data. A correlation matrix is commonly applied to risks or capital amounts and is an important determinant of calculated risk capital, including levels of diversification. |

Dependency Structure | Methods | United States | NAIC ORSA MANUAL | Specification of the relationship between different variables. Commonly specified in a correlation matrix. |

Diversification | Methods | International Risk Management Institute | IRMI Terms | A risk control technique that spreads loss exposures over a myriad of projects, products, areas, or markets. |

Diversification | Methods | The European Economic Area | Solvency II | 'Diversification effects' means the reduction in the risk exposure of insurance and reinsurance undertakings and groups related to the diversification of their business, resulting from the fact that the adverse outcome from one risk can be offset by a more favourable outcome from another risk, where those risks are not fully correlated. (Solvency II Directive art. 13(37) |

Probability of Ruin | Methods | International Risk Management Institute | IRMI Terms | The percentile of the probability distribution corresponding to the point at which capital is exhausted. Typically, a minimum acceptable probability of ruin is specified, and economic capital is derived therefrom. |

Probability of Ruin | Methods | The European Economic Area | CEA Solvency II | Risk measure. The likelihood that total net cash outflows exceed at any time the available resources starting with a given amount of resources, within a specified time horizon. |

Probability of Ruin | Methods | The European Economic Area | Solvency II | 'Risk measure' means a mathematical function which assigns a monetary amount to a given probability distribution forecast and increases monotonically with the level of risk exposure underlying that probability distribution forecast.(Solvency II Directive art. 13(39)) |

Probability of Ruin | Methods | United States | NAIC ORSA MANUAL | Likelihood of liabilities exceeding assets for a given time horizon. |

Reverse Stress Testing | Methods | COSO | COSO | The possibility that events will occur and affect the achievement of strategy and business objectives |

Reverse Stress Testing | Methods | IAIS | IAIS ICP 16 | Reverse stress testing identifies scenarios that are most likely to cause an insurer to fail. Such an approach may help to ensure adequate focus on the management actions that are appropriate to avoid undue risk of business failure. The focus of such reverse stress testing may be largely qualitative in nature although broad assessment of associated financial impacts may help in deciding the appropriate action to take. |

Reverse Stress Testing | Methods | International Actuarial Association | IAA ISAP | A process for identifying events or scenarios that would lead to a predetermined financial indicator for an organization (draft) |

Reverse Stress Testing | Methods | The European Economic Area | Solvency II | The term is mentioned in the Guidelines on the ORSA, but has not been defined explicitly. |

Scenario Analysis | Methods | IAIS | IAIS Supervisory Material | A complicated type of test, which contains simultaneous moves in a number of risk factors and is often linked to explicit changes in the view of the world. |

Scenario Analysis | Methods | The European Economic Area | CEA Solvency II | Simulation of an alternative set of parameters within a model in order to establish the impact on the outcome. |

Scenario Analysis | Methods | The European Economic Area | Solvency II | The term is mentioned in the Guidelines on the ORSA, but has not been defined explicitly. |

Scenario Analysis | Methods | United States | NAIC ORSA MANUAL | Analysis of the impact of possible future outcomes, based on alternative projected assumptions. This can include changes to a single assumption or combination of assumptions. |

Scenario Analysis | Methods | United States | U.S. ASB Terms | (Scenario Test) A process for assessing the impact of one possible event or seveal simultaneously or sequentially occuring possible events on an organization's financial position. |

Stochastic Analysis | Methods | IAIS | IAIS Supervisory Material | A methodology which aims at attributing a probability distribution to financial variables of interest. It sometimes uses closed form solutions, often involves simulating large numbers of scenarios in order to reflect the distributions of the capital required by, and the different risk exposures of, the insurer. |

Stochastic Analysis | Methods | United States | NAIC ORSA MANUAL | A methodology designed to attribute a probability distribution to a range of possible assumptions. This can include changes to a single assumption or combination of assumptions. |

Stress Test | Methods | IAIS | IAIS ICP 16 | The method of measuring the financial impact of stressing one or relatively few factors affecting the insurer. |

Stress Test | Methods | IAIS | IAIS Supervisory Material | The method of solvency assessment that provides for the consideration of the impact (current and prospective) of a particular defined set of alternative assumptions or outcomes that are adverse. Consideration is given to the effect on the insurance company assets, liabilities and operations of a defined adverse scenario. |

Stress Test | Methods | International Actuarial Association | IAA ISAP | A process for assessing the impact of one possible event or several simultaneously or sequentially occurring possible events on an entity's financial position (draft). |

Stress Test | Methods | The European Economic Area | CEA Solvency II | A type of scenario analysis in which the change in parameters are considered significant, or even extreme. |

Stress Test | Methods | The European Economic Area | Solvency II | The term is mentioned in the Guidelines on the ORSA, but has not been defined explicitly. |

Stress Test | Methods | United States | NAIC ORSA MANUAL | A type of scenario analysis in which the change in parameters is considered significantly adverse or even extreme. |

Stress Test | Methods | United States | U.S. ASB Terms | A process for measuring the impact of adverse changes in one or relatively few factors affecting an organization's financial position. |

Time Horizon | Methods | International Actuarial Association | IAA - Acturial Aspects of ERM for Insurance Companies | The time period associated with a given decision or measure. |

Time Horizon | Methods | The European Economic Area | CEA Solvency II | The period over which any amount of required capital is held in order to cover losses, within a given risk tolerance level. |

Time Horizon | Methods | United States | NAIC ORSA MANUAL | In the context of risk capital calculations, the period over which the impact of changes to risks is tested. |

Value-at-Risk (see also TailVaR) | Methods | IAIS | IAIS Supervisory Material | An estimate of the worst expected loss over a certain period of time at a given confidence level. |

Value-at-Risk (see also TailVaR) | Methods | International Actuarial Association | IAA - Acturial Aspects of ERM for Insurance Companies | The maximum loss that could occur with a specified probability over a given time horizon. |

Value-at-Risk (see also TailVaR) | Methods | International Risk Management Institute | IRMI Terms | The worst loss expected over a target horizon within a given confidence interval. |

Value-at-Risk (see also TailVaR) | Methods | The European Economic Area | CEA Solvency II | Value-at-risk is a quantile of a distribution and used as a (non-coherent) risk measure. |

Value-at-Risk (see also TailVaR) | Methods | The European Economic Area | Solvency II | The term is mentioned in the Directive, but has not been defined explicitly. Article 104.4 says: Each of the risk modules referred to in paragraph 1 shall be calibrated using a Value-at-Risk measure, with a 99,5 % confidence level, over a one-year period. |

Value-at-Risk (see also TailVaR) | Methods | United States | NAIC ORSA MANUAL | An estimate of the maximum loss over a certain period of time at a given confidence level. |