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Per-Asset Beta to a Benchmark Portfolio

Basel III Output Floor — Capital Requirement Across Phase-In Schedule

Basel IRB Risk-Weighted Asset for a Corporate Exposure

Basel VaR Backtest Traffic-Light Zones

Basel VaR Backtest — Traffic-Light Zone and Capital Multiplier Add-On

Bilateral CVA and DVA Under Independence: Two Discounted Time-Profile Sums

Analytical Binomial Credit-Loss VaR for a Uniform-PD Homogeneous Portfolio

Box-Muller: Uniform Pairs to Standard-Normal Pairs

Brinson-Hood-Beebower Three-Effect Attribution

Calmar Ratio — Annualized Return over Maximum Drawdown

Capital Conservation Buffer: MDA Factor Quartile Schedule

Per-Tenor Flat-Hazard Survival Curve from a CDS Spread Term Structure

Implied Default Probability from a CDS Spread

CDS-Implied Cumulative Default Probability via the Credit-Triangle Approximation

Par CDS Spread Implied by a Cumulative Default Probability via the Inverse Credit Triangle

CDS Upfront Fee from Par Spread, Standard Coupon, and Risky PV01

Choueifaty Diversification Ratio of a Gaussian Portfolio

Christoffersen Conditional Coverage LR_cc Joint Statistic for VaR Backtesting

Christoffersen LR_ind Independence Statistic for VaR Backtesting

Christoffersen Independence Test for VaR Breach Clustering

Sample from a Clayton Copula

Component VaR Decomposition (Euler Allocation)

Component VaR Decomposition for a Gaussian Portfolio

Compound-Poisson Aggregate-Loss Variance for an Operational-Risk LDA Period

Conditional Drawdown at Risk

Conditional Scenario-Tree Probability-Weighted PnL Aggregation

Empirical Copula Tail-Dependence Coefficients

Cornish-Fisher VaR

Cornish-Fisher VaR Adjusted for Skewness and Excess Kurtosis

Aggregate Multi-Desk VaR from Standalone VaRs and a Loss-Correlation Matrix

Correlated Factor-Shock Monte-Carlo for Stress P&L

Credit Expected Loss under Multiplicative PD and LGD Stress Shocks

Credit Portfolio Expected Loss and Naive Unexpected Loss

Credit Portfolio Concentration: HHI and Effective Number of Counterparties from Per-Obligor EAD

Credit Portfolio MC Loss Distribution (Single-Factor Gaussian Copula)

Cross-Gamma 2D Shock-Grid PnL via Bilinear-Quadratic Taylor

Cumulative Default Probability from Marginal Hazard Rates: Term-Structure Composition

Pairwise Default Correlation from One-Factor Gaussian-Copula Bivariate-CDF Inputs

Diebold-Mariano Test for Two VaR Forecasts via Pinball-Loss Differential

PV-Weighted Effective Maturity M for IRB Credit RWA Input

Effective Number of Independent Obligors from Uniform Pairwise Default Correlation

Empirical CDF Tail Probability at a Fixed PnL Threshold

Empirical Copula via Per-Column Uniform Rank Transform

Empirical Inverse-CDF Marginal Mapping (Copula Pipeline, Step Two)

Empirical Mean Excess Function for POT Threshold Selection

Empirical Upper-Tail-Dependence Coefficient from Bivariate Samples

Expected Shortfall Calibration Backtest via Exceedance-Day Ratio

Euler Risk Allocation for Portfolio Volatility

Fit a Gumbel (GEV, ξ=0) to Block Maxima by Method of Moments

Hill Estimator for the Tail Index

Peaks-Over-Threshold GPD Fit by Method of Moments

RiskMetrics EWMA Volatility Forecast

EWMA-Weighted Historical VaR

Expected Portfolio RWA After H Rating-Migration Steps

Rolling Historical Expected Shortfall (CVaR)

Per-Factor Risk Attribution Under a Linear Factor Model

Factor-Shock Scenario P&L on a Linear Factor Model

Filtered Historical Simulation VaR

GARCH(1,1) Multi-Step Variance Forecast

Gaussian-Copula Correlated Samples via Cholesky Factorisation

Sample from a Gaussian Copula

GPD Tail-VaR Extrapolation under the POT Framework

G-SIB Systemic-Importance Score with Substitutability Cap

Bivariate Gumbel-Copula CDF Closed-Form Evaluation

Hill Estimator for the Tail Index of a Heavy-Tailed Loss Distribution

Historical Expected Shortfall at Multiple Confidence Levels

Historical Expected Shortfall

Historical Scenario Replay: Worst-K Rolling-Window PnLs

Historical Stress Loss Replay

Historical VaR at Multiple Confidence Levels

Historical VaR for a Long-Only Portfolio

Rolling Historical VaR Track

Component VaR per Asset (Euler Decomposition)

Incremental VaR of a Candidate Trade

Information Ratio of an Active-Return Series

Kendall's Tau-a Rank Correlation on a Bivariate Sample

Kupiec POF Likelihood-Ratio Statistic for VaR Backtesting

Kupiec Proportion-of-Failures (POF) Test Statistic

Basel III Liquidity Coverage Ratio with HQLA Caps

Basel III Leverage Ratio

Basel III Leverage Ratio: Credit Conversion Factors over Off-Balance Items

LGD Beta-Distribution Calibration via Method of Moments

LGD via Collateral-Then-Unsecured Recovery Waterfall

LGD Aggregation with Collateral Recovery Cascade

Lifetime Expected Loss with Survival Weighting and Per-Period LGD/EAD

Liquidity Coverage Ratio: HQLA, Inflow Cap, and Net-Outflow Floor

Lopez I Magnitude Loss Function for VaR Backtesting

Mahalanobis Distance via Cholesky Forward-Solve

Marginal Default Probability from a Cumulative-PD Term Structure: Inverse Bootstrap

Marginal VaR by Asset (Closed-Form Gradient)

Marginal VaR Sensitivity for a Gaussian Portfolio

Maximum Drawdown Duration on the Equity Curve

Mean-Excess Curve Across a Threshold Grid

Mincer-Zarnowitz OLS Regression for VaR-Forecast Unbiasedness

Modigliani M-Squared — Vol-Rescaled Risk-Adjusted Return

Monte-Carlo VaR for a Multi-Asset Portfolio

Multi-Horizon Gaussian VaR Scaling

Multi-Factor Scenario PnL Vector via Linear Taylor

Net Stable Funding Ratio: ASF over RSF Aggregation

Basel III Net Stable Funding Ratio (NSFR)

Omega Ratio of a Return Series at a Threshold

Pairwise Rating-Transition Probability at Horizon: Single Entry of Markov Chain M^H

Parametric Gaussian Expected Shortfall from Caller-Supplied Moments

Rolling Parametric VaR (Normal)

Pareto Tail VaR via Hill-Estimator Extrapolation

Multi-Period Default Probability from a Rating-Transition Matrix

Survival Probability at Multiple Horizons under a Piecewise-Flat Hazard Term Structure

Pinball (Quantile) Loss for VaR Forecast Backtesting

Standardized VaR-Forecast Residual Stream — De-Mean Then Divide By Vol

Portfolio Expected Loss by Bucket: PD x LGD x EAD Waterfall

Multi-Asset Portfolio Parametric VaR (w^T Σ w)

Present Value of a Post-Default Recovery Cash-Flow Stream

Quadratic-Taylor Scenario PnL Vector via Delta and Gamma

Spearman Rho and Kendall Tau-b: Dual Rank-Correlation Diagnostic for the Copula Pipeline

Multi-Step Rating Distribution Propagation: Markov Transition Forward H Steps

Realized-Volatility Jump Test (Barndorff-Nielsen and Shephard)

Regime-Conditional Historical Expected Shortfall

Regime-Conditional Historical VaR

Reverse Stress Test — Flag Scenarios That Hit a Loss Target

Reverse Stress Test — Solve for Shock Magnitude Hitting a Target Loss

Risk-Budget Allocation via Iterative Fixed-Point

Rolling-Window Variance Ratio Test (Lo-MacKinlay)

SA-CCR Counterparty EAD: Collateral-Adjusted RC plus Aggregated PFE with Alpha

Semi-Deviation of a Return Series Around the Sample Mean

Single-Name Concentration: Flag Counterparties Breaching the Basel Large-Exposure Limit

Sortino Ratio of a Return Series with Target Return

Spectral Risk Measure (Acerbi 2002)

Stress Coverage Ratios Against Available Capital

Stress Impact on CET1 Ratio: Stressed Ratio and Change-from-Baseline

Stress-Loss Aggregation by Bucket

Stressed Expected Shortfall — Worst Rolling-Window Historical ES

Stressed VaR — Worst Rolling-Window Historical VaR

Survival-Weighted Expected-Exposure Profile for CVA Aggregation

Systematic-vs-Idiosyncratic Variance Decomposition (Factor Model)

t-Copula Correlated Samples via Cholesky and Chi-Square Scaling

Through-the-Cycle PD from a Point-in-Time Series: Geometric Mean of Survivals

Tier-1 Capital Ratio: CET1 Deductions, AT1 Add-back, and RWA

FSB TLAC Dual Ratios: TLAC/RWA and TLAC/Leverage-Exposure

Tracking-Error Variance Contribution by Sector

Scalar Tracking Error of an Active-Return Series

Treynor Ratio — Systematic-Risk-Adjusted Excess Return

Unilateral CVA Under PD-EE Independence: Discounted Time-Profile Sum

Up-Capture and Down-Capture Ratios versus a Benchmark

VaR Backtest Exceedance Count and Longest Cluster

Count and Timestamp VaR Breaches

Lag-1 Autocorrelation of VaR Hit Indicators

Vasicek ASRF Loss Rate

Vasicek Single-Factor Conditional PD Given a Realized Systematic Factor

Vasicek ASRF Capital Factor at Confidence Level Alpha (Basel IRB)

Vintage Cohort Per-Period Default Rate: Conditional Hazard from a Loan Vintage

Weighted Historical VaR with Custom Weights

Wilson Score Binomial CI for VaR Exceedance Rate