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Add Two Binary Strings

Multi-Feed Bar-Sync Period: LCM Modulo p

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

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

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

Per-Position Flag Bitmask Queries

Periodic Yield To Maturity of a Fixed-Rate Coupon Bond via Bisection

Box-Muller: Uniform Pairs to Standard-Normal Pairs

Capital Conservation Buffer: MDA Factor Quartile Schedule

Card Shuffle Bias Detection

Periodic IRR of an Equally-Spaced Cashflow Stream Under the Standard-Project Assumption via Bisection

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

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

Christoffersen Conditional Coverage LR_cc Joint Statistic for VaR Backtesting

Christoffersen LR_ind Independence Statistic for VaR Backtesting

Conditional Scenario-Tree Probability-Weighted PnL Aggregation

Credit Expected Loss under Multiplicative PD and LGD Stress Shocks

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

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

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

Cumulative VWAP at Each Tick

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

Expected Shortfall Calibration Backtest via Exceedance-Day Ratio

RiskMetrics EWMA Volatility Forecast

EWMA-Weighted Historical VaR

Expected Portfolio RWA After H Rating-Migration Steps

Filtered Historical Simulation VaR

FizzBuzz

GARCH(1,1) Multi-Step Variance Forecast

Gaussian-Copula Correlated Samples via Cholesky Factorisation

GCD of Share Lots — Round-Lot Reconciliation

Universal Tick Unit: GCD of Per-Venue Tick Sizes

G-SIB Systemic-Importance Score with Substitutability Cap

Bivariate Gumbel-Copula CDF Closed-Form Evaluation

Historical Expected Shortfall at Multiple Confidence Levels

Historical Expected Shortfall

Historical VaR at Multiple Confidence Levels

Kupiec POF Likelihood-Ratio Statistic for VaR Backtesting

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

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

Disjoint Risk-Bucket Hedge Selection under a Bucket-Budget Bitmask

Mean-Excess Curve Across a Threshold Grid

Min Contracts to Cover Greek Buckets via Bitmask BFS

Mincer-Zarnowitz OLS Regression for VaR-Forecast Unbiasedness

Misra-Gries (k-1)-Counter Heavy-Hitters Over a Trade-Tape Stream

Multi-Horizon Gaussian VaR Scaling

Multi-Factor Scenario PnL Vector via Linear Taylor

Net Stable Funding Ratio: ASF over RSF Aggregation

Lag-1 Sample Autocorrelation of a Time Series

Online Cumulative Bollinger Bands: Welford-Recurrence Band-Pair Stream

Online EWMA Covariance Pair — Cross-Asset Hedge-Ratio Building Block

Online EWMA Residual Stream — Surprise-vs-Prior Exponential-Weight Mean

Online EWMA Variance — Recency-Weighted Volatility Tracker

Running Mean and Mean Absolute Deviation

Online Running Excess Kurtosis via Welford-Style Fourth-Moment Recurrence

Online Running Sample Skewness via Welford-Style Third-Moment Recurrence

Online Streaming Mean, Variance, Skewness, and Excess Kurtosis (Welford-Pebay)

Online Z-Score Outlier Flagger: Welford-Cumulative Anomaly Detection on a Tick Stream

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

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

Power-of-Two Bit Check

Primality Test by Trial Division

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

Quadratic-Taylor Scenario PnL Vector via Delta and Gamma

Rank Strategies by Sharpe with Vol Tiebreak

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

Regime-Conditional Historical Expected Shortfall

Regime-Conditional Historical VaR

Reverse Stress Test — Flag Scenarios That Hit a Loss Target

Running Maximum Drawdown of a Streamed Log-Return NAV Path

Running Min and Max of a Stream

Running Cumulative-History Pearson Correlation via Welford-Style Co-Moment Recurrence

P-Square (P²) Streaming Quantile Estimator

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

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

Smallest Position Size Meeting Risk Budget

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

Stressed Expected Shortfall — Worst Rolling-Window Historical ES

Subranges Above Return Threshold

Survival-Weighted Expected-Exposure Profile for CVA Aggregation

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

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

VaR Backtest Exceedance Count and Longest Cluster

Lag-1 Autocorrelation of VaR Hit Indicators

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

Welford Warm-up-Trimmed Sample Variance — Stable Online Estimator on a Trailing Tail

Wilson Score Binomial CI for VaR Exceedance Rate