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📊 '''Value-at-risk (VaR)''' is a statistical measure used extensively in the insurance and financial services industries to quantify the maximum expected loss on a portfolio or balance sheet over a specified time horizon at a given confidence level. In insurance, VaR serves as a foundational tool for [[Definition:Enterprise risk management (ERM) | enterprise risk management]] and [[Definition:Regulatory capital | regulatory capital]] determination, helping insurers and [[Definition:Reinsurance | reinsurers]] understand the tail risks embedded in their [[Definition:Underwriting | underwriting]] portfolios, [[Definition:Investment portfolio | investment portfolios]], and [[Definition:Reserving | reserve]] positions. Under [[Definition:Solvency II | Solvency II]], for instance, the [[Definition:Solvency capital requirement (SCR) | solvency capital requirement]] is explicitly calibrated to a one-year VaR at the 99.5% confidence level, meaning insurers must hold enough capital to withstand all but the worst one-in-two-hundred-year loss scenarios. Other regimes, such as the [[Definition:Risk-based capital (RBC) | risk-based capital]] framework administered by the [[Definition:National Association of Insurance Commissioners (NAIC) | NAIC]] in the United States or China's [[Definition:China Risk Oriented Solvency System (C-ROSS) | C-ROSS]], incorporate VaR-like concepts even when the precise calibration methodology differs.

⚙️ Calculating VaR in an insurance context involves selecting a confidence level, a time horizon, and a method for estimating the loss distribution. The three most common approaches are the historical simulation method, which uses observed past losses; the variance-covariance (parametric) method, which assumes a normal or other specified distribution; and [[Definition:Monte Carlo simulation | Monte Carlo simulation]], which generates thousands of hypothetical scenarios to model complex, non-linear risks. For a property-catastrophe insurer, VaR might be computed using [[Definition:Catastrophe model | catastrophe models]] that simulate hurricane or earthquake events across a book of business, while a life insurer might focus on interest rate and longevity risk within its [[Definition:Liability | liabilities]]. Insurers using [[Definition:Internal model | internal models]] under Solvency II must demonstrate to supervisors that their VaR calculations are robust, well-validated, and integrated into actual decision-making — a requirement known as the "use test." One widely acknowledged limitation is that VaR does not describe the magnitude of losses beyond the chosen threshold, which is why regulators and risk managers often supplement it with [[Definition:Tail value-at-risk (TVaR) | tail value-at-risk (TVaR)]], also known as conditional VaR or expected shortfall, which averages all losses exceeding the VaR boundary.

💡 The prominence of VaR in insurance regulation and risk management has reshaped how insurers allocate capital, price risk, and communicate with stakeholders. By translating complex risk exposures into a single monetary figure, VaR enables boards and senior management to compare risks across disparate lines of business — say, [[Definition:Cyber insurance | cyber liability]] versus [[Definition:Motor insurance | motor insurance]] — on a common basis. [[Definition:Rating agency | Rating agencies]] such as [[Definition:AM Best | AM Best]] and [[Definition:Standard & Poor's (S&P) | S&P]] evaluate VaR-based capital models when assessing an insurer's financial strength, and investors in [[Definition:Insurance-linked securities (ILS) | insurance-linked securities]] rely on VaR disclosures to gauge exposure. However, the 2007–2008 financial crisis exposed dangers of over-reliance on VaR — particularly when correlations spike during market stress — prompting regulators worldwide to demand more sophisticated stress-testing and scenario analysis alongside VaR-based metrics. In the insurance sector, this evolution has encouraged a more holistic approach to [[Definition:Own risk and solvency assessment (ORSA) | own risk and solvency assessment]] processes, where VaR remains a core metric but is no longer treated as the sole arbiter of risk.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Tail value-at-risk (TVaR)]]
* [[Definition:Solvency capital requirement (SCR)]]
* [[Definition:Enterprise risk management (ERM)]]
* [[Definition:Internal model]]
* [[Definition:Catastrophe model]]
* [[Definition:Own risk and solvency assessment (ORSA)]]
{{Div col end}}

Definition:Value-at-risk (VaR) - Revision history

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