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Add Two Binary Strings

Shrinkage Blend of Two Alpha Sources with Z-Score Normalization

American Put Pricing via Longstaff-Schwartz Least-Squares Monte Carlo

Antithetic Variates Variance Reduction

Dual-Benchmark IS — Arrival Price vs Interval VWAP

Arithmetic-average Asian Call MC Pricing with Antithetic Variates

Geometric-average Asian Call: Closed-form Black-Scholes Pricing

Per-Asset Beta to a Benchmark Portfolio

Bachelier (Normal) Implied Vol from a Quoted Call

Multi-Feed Bar-Sync Period: LCM Modulo p

Up-and-out Barrier Call MC Pricing with Daily Monitoring

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

CRR Binomial Tree for an American Put

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

CRR Binomial Tree for a European Call

Black-Scholes Call Implied Vol via Bisection

Per-Position Flag Bitmask Queries

Convexity of a Fixed-Coupon Bond

Modified Duration of a Fixed-Coupon Bond

Modified Duration on a Discrete Zero Curve

Bond Portfolio Key-Rate Duration Hedge via Least Squares

Continuous-Compounded Yield-to-Maturity for a Fixed-Coupon Bond

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

Box-Muller: Uniform Pairs to Standard-Normal Pairs

Brinson-Hood-Beebower Three-Effect Attribution

Brownian Bridge Running Minimum Survival Probability

Black-Scholes Delta for Batched Calls and Puts

Black-Scholes European Call and Put Pricing in Batch

Black-Scholes Gamma and Vega in Batch

Black-Scholes Implied Vol from a Quoted Call or Put via Newton-Raphson

Black-Scholes Rho for Batched Calls and Puts

Black-Scholes Theta for Batched Calls and Puts

Detect Butterfly-Arbitrage Violations on a Call-Price Strike Grid

Calmar Ratio — Annualized Return over Maximum Drawdown

Capital Conservation Buffer: MDA Factor Quartile Schedule

Card Shuffle Bias Detection

Cash-or-Nothing Digital Call: Closed-form Black-Scholes Pricing

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

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

CIR Short-Rate MLE Calibration on a Historical Series

Sample from a Clayton Copula

Locally-capped Cliquet Call MC Pricing with Antithetic Variates

Component VaR Decomposition (Euler Allocation)

Component VaR Decomposition for a Gaussian Portfolio

IC-IR-Weighted Composite of Three Sub-Factors

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

Conditional Drawdown at Risk

Conditional Scenario-Tree Probability-Weighted PnL Aggregation

European Call MC with Geometric-Asian Control Variate

Empirical Copula Tail-Dependence Coefficients

Cornish-Fisher VaR

Cornish-Fisher VaR Adjusted for Skewness and Excess Kurtosis

Covariance to Correlation Matrix

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

Cross-Gamma PnL Attribution: Two-Asset Greek Decomposition

Cross-Sectional Demean of an Alpha Factor

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

Bump-and-Revalue Finite-Difference Delta

Discrete Delta-Hedge Path Simulation with Transaction Costs

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

Digital Cash-or-Nothing Call Monte Carlo with Antithetic Variates

Dollar Gamma Across a Strike Ladder

Double-No-Touch Pricing via Antithetic-Variate Monte Carlo

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

Equal-Risk-Contribution Portfolio Weights

Toy Equal-Risk-Contribution Solver (Fixed-Point Iteration)

Expected Shortfall Calibration Backtest via Exceedance-Day Ratio

Estimate Barrier Hit Probability

Euler Risk Allocation for Portfolio Volatility

European Call Monte Carlo with Antithetic Variates

European Call Price via Monte Carlo

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

Exponentially-Weighted Sharpe Ratio

RiskMetrics EWMA Volatility Forecast

EWMA Volatility Update

EWMA-Weighted Historical VaR

Excess Returns Over a Benchmark

Composite Broker Execution-Quality Score with Direction-Aware Z-Score Blend

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

Per-Venue Fill Rate with Wilson Confidence Intervals

Filtered Historical Simulation VaR

OU First-Passage Time by Monte Carlo

Fixed-strike Lookback Call MC Pricing with Discrete Monitoring

FizzBuzz

Pricing a Floating-Rate Note from a Zero Curve

Cross-Hedge Residual Variance and Explanatory Power

Black-Scholes PnL Attribution: Delta, Gamma, Vega, Theta

GARCH(1,1) Multi-Step Variance Forecast

Gaussian-Copula Correlated Samples via Cholesky Factorisation

Sample from a Gaussian Copula

GCD of Share Lots — Round-Lot Reconciliation

Universal Tick Unit: GCD of Per-Venue Tick Sizes

Greenwald-Khanna Streaming Quantile Summary

GPD Tail-VaR Extrapolation under the POT Framework

G-SIB Systemic-Importance Score with Substitutability Cap

Bivariate Gumbel-Copula CDF Closed-Form Evaluation

HDR Histogram Recorded-Value Bucket Index and Quantile Estimate

Single-Sigma Black-Scholes Calibration to a Strike Grid

Heston Calibration Residual in Implied-Vol Space

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

Historical Expected Shortfall at Multiple Confidence Levels

Historical Expected Shortfall

Historical Stress Loss Replay

Historical VaR at Multiple Confidence Levels

Historical VaR for a Long-Only Portfolio

Rolling Historical VaR Track

IC-Weighted Alpha Signal Combination

Idiosyncratic Volatility Factor — Rolling Residual Std After Market Beta

Post-Trade Impact Attribution Across Venues with a Cross-Venue Interaction

Implementation Shortfall — Three-Component Attribution

Implied Volatility with Newton + Bisection Fallback

Newton-Raphson Implied Volatility from a Quoted Call

Vega-Weighted Average Implied Volatility Across a Strike Grid

Implied Volatility via Bisection

Implied Volatility via Newton's Method

Importance Sampling for Deep OTM Monte Carlo

Component VaR per Asset (Euler Decomposition)

Incremental VaR of a Candidate Trade

Annualized Information Ratio

Information Ratio of an Active-Return Series

Black-Scholes Call Implied Vol via Brent's Method (scipy.optimize.brentq)

Black-Scholes Call Implied Vol via Hybrid Newton-Raphson with Bisection Fallback

Batch IV Pre-Flight — No-Arbitrage Bracket Classifier

Black-Scholes Put Implied Vol via Bisection

Black-Scholes Call Implied Vol via the Secant Method

Merton Jump-Diffusion European Call via Monte Carlo

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

Linear Market-Impact Cost of a Child-Order Schedule

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

Look-Ahead Bias Detector via Lagged-Correlation Comparison

Fixed-Strike Lookback Call Pricing via Monte Carlo

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-Diversification Portfolio (Choueifaty-Coignard)

Max Drawdown Decomposition

Maximum Drawdown Duration on the Equity Curve

Semi-Analytic Call Price on the Max of n iid Lognormals

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

Mean-Excess Curve Across a Threshold Grid

Mean-Reversion Factor — Residualized Last-K Return

Long-Only Mean-Variance Efficient Frontier

Min Contracts to Cover Greek Buckets via Bitmask BFS

Two-Asset Minimum-Variance Portfolio (Closed Form)

Long-Only Minimum-Variance Portfolio Weights

Mincer-Zarnowitz OLS Regression for VaR-Forecast Unbiasedness

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

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

Monte-Carlo VaR for a Multi-Asset Portfolio

Multi-Horizon Gaussian VaR Scaling

Multi-Leg Implementation Shortfall — Basket Covariance Attribution

Multi-Level Monte Carlo for a European Call

Multi-Period Impact P&L with Exponential Decay Between Periods

Multi-Factor Scenario PnL Vector via Linear Taylor

Rank Features by Histogram-Estimated Mutual Information with the Target

Net Stable Funding Ratio: ASF over RSF Aggregation

Basel III Net Stable Funding Ratio (NSFR)

Omega Ratio of a Return Series at a Threshold

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 PCA via Oja's Rule (Streaming PC1)

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

Classical Gram-Schmidt Orthogonalization of Priority-Ordered Alpha Signals

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

Closed-Form 2x2 PCA Eigendecomposition

PCA Explained-Variance Ratio for Top-k Components

Optimal Ledoit-Wolf Shrinkage (Frobenius)

Multi-Period Default Probability from a Rating-Transition Matrix

Percent-Change from a Configurable Base

Quantile Estimate from Pre-Bucketed Histogram Counts

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

Greek-Based PnL Attribution

Greek-Attribution P&L Explain with Residual Diagnostic

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

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

Position P&L With Transaction Fees

Power-of-Two Bit Check

Pre-Trade Multi-Leg Impact Budget Check (Square-Root Model)

Primality Test by Trial Division

Purged k-Fold Cross-Validation for Time-Series ML

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

Quadratic-Taylor Scenario PnL Vector via Delta and Gamma

Best-of-N Rainbow Call MC Pricing with Cholesky and Antithetic Variates

Random Walk Hitting Probability

Range-Accrual Note Pricer via Daily-Monitoring MC with Antithetic Variates

Rank-Average Multi-Factor Signal Combination

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

RankGauss Transform on a Cross-Section of Alpha Factors

Rank Strategies by Sharpe with Vol Tiebreak

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 Beta — Strategy vs. Benchmark

Rolling Beta vs Benchmark

Rolling Engle-Granger Cointegration Test for Pairs Trading

Rolling Pearson Correlation Between Two Series

Rolling-Window Variance Ratio Test (Lo-MacKinlay)

Rolling Z-Score Anomaly Flags

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

Hagan SABR Implied Lognormal Vol from Parameters

Calibrate SABR Volvol (alpha, rho, nu) to a Smile

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

Semi-Deviation of a Return Series Around the Sample Mean

Implementation Shortfall — Fee vs Market-Impact Decomposition

Toy Ledoit-Wolf Shrinkage Covariance

Multi-Horizon Signal Blend with Time Decay

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

Size Factor as Negative Log Market Cap (Cross-Sectional Z-Score)

Smallest Position Size Meeting Risk Budget

Annualized Sortino Ratio

Sortino Ratio of a Return Series with Target Return

Spectral Risk Measure (Acerbi 2002)

Fit the Square-Root Market-Impact Coefficient by Weighted Least-Squares

European Call MC with Stratified Sampling on Terminal Z

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

Subranges Above Return Threshold

Survival-Weighted Expected-Exposure Profile for CVA Aggregation

Svensson (1994) 6-Parameter Yield-Curve Fit

SVI Slice Fit with No-Butterfly-Arbitrage Constraint

Fit SVI Parameters to a Single Expiry Slice

Systematic-vs-Idiosyncratic Variance Decomposition (Factor Model)

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

Target-Volatility Scaling with Leverage Cap

T-Digest Streaming Percentile Estimator (k_1 Scale Function)

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

Trailing 12-1 Momentum Factor (Skip Last Month)

Transaction-Cost-Aware Target Weights from Alpha Signal

Treynor Ratio — Systematic-Risk-Adjusted Excess Return

CRR3 Trinomial Tree for a European Call

Turnover-Constrained Portfolio Rebalance

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

Up-and-In Barrier Call: Closed-form Reiner-Rubinstein Pricing with Rebate

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 MLE Fit from a Short-Rate Series

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

Vasicek Short-Rate MLE Calibration on a Historical Series

Vega-Bucketed PnL Explain Across a Strike Grid

Static Vega Replication of an Exotic into a Vanilla Basis

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

Detect Calendar-Arbitrage Violations on an Implied-Vol Surface

Linear Total-Variance Interpolation Across Maturities

Inverse-Vol Portfolio with Position Cap

VWAP Deviation by Broker

Walk-Forward Train/Test Splits with Embargo

Walk-Forward Validation for Time-Series Backtests

Weighted Historical VaR with Custom Weights

Welford's Online Variance

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

Wilson Score Binomial CI for VaR Exceedance Rate

Cross-Sectional Winsorization of Alpha-Factor Values

Bootstrap a Zero Curve from Par Yields

Yield to Maturity via Bisection

Cross-Sectional Z-Score with Optional Winsorization