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

Antithetic Variates Variance Reduction

Arithmetic-average Asian Call MC Pricing with Antithetic Variates

As-of Merge — Attach Most-Recent Mid-Price to Each Trade

As-of Merge — Trades against Quotes

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

Backward Induction on a Generic Binary Tree

Invert Binary Tree (Mirror)

Maximum Depth of a Binary Tree (Recursive)

Symmetric Binary Tree Check

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

American Put Pricing on a CRR Binomial Tree

Blocked Time-Respecting CV: Contiguous Folds with Train-Before-Test

Box-Muller: Uniform Pairs to Standard-Normal Pairs

Brownian Bridge Running Minimum Survival Probability

Card Shuffle Bias Detection

Christoffersen Conditional Coverage LR_cc Joint Statistic for VaR Backtesting

Christoffersen LR_ind Independence Statistic for VaR Backtesting

Sample from a Clayton Copula

Locally-capped Cliquet Call MC Pricing with Antithetic Variates

Cluster Correlated Tickers

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

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

Factor Cluster Count: Connected Components on a Thresholded Correlation Graph

Win-Count Leaves on a Forward Scenario Tree

Count Regime Paths Satisfying Constraint

Cumulative PnL Zero-Crossings: Count Sign Flips of the Backtest Equity Curve

Recursive Binary Decision-Tree Evaluator

Deepest No-Drawdown Leaf on a Forward Scenario Tree

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

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

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

Earliest K-Day Window Whose Population Variance Strictly Exceeds A Spike Threshold

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

Estimate Barrier Hit Probability

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

Rolling Historical Expected Shortfall (CVaR)

Expected Value at Root of Scenario Tree

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

Cross-Hedge Residual Variance and Explanatory Power

GARCH(1,1) Multi-Step Variance Forecast

Gaussian-Copula Correlated Samples via Cholesky Factorisation

Sample from a Gaussian Copula

Greenwald-Khanna Streaming Quantile Summary

GPD Tail-VaR Extrapolation under the POT Framework

Groupby-Mean by Key with a Min-Count Gate

Bivariate Gumbel-Copula CDF Closed-Form Evaluation

HDR Histogram Recorded-Value Bucket Index and Quantile Estimate

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

Idiosyncratic Volatility Factor — Rolling Residual Std After Market Beta

Importance Sampling for Deep OTM Monte Carlo

Incremental Largest Cluster Size: Streaming Union-Find on a Factor-Pair Edge Tape

Component VaR per Asset (Euler Decomposition)

Annualized Information Ratio

Inverse Percentile Rank of Daily PnL Against Reference Distribution

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

Lag/Lead Shift by Key — Within-Group Time-Series Offset

Largest Factor Cluster Size: Maximum Connected Component on a Thresholded Correlation Graph

LGD Beta-Distribution Calibration via Method of Moments

Longest Stable Trading Streak

Longest Sub-Window Beating a PnL Target via Monotonic-Stack on Prefix Sums

Look-Ahead Bias Detector via Lagged-Correlation Comparison

Mahalanobis Distance via Cholesky Forward-Solve

Max Drawdown Decomposition

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

Mean-Excess Curve Across a Threshold Grid

Mean-Reversion Factor — Residualized Last-K Return

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

Monte-Carlo VaR for a Multi-Asset Portfolio

Multi-Horizon Gaussian VaR Scaling

Multi-Level Monte Carlo for a European Call

Multi-Factor Scenario PnL Vector via Linear Taylor

Rank Features by Histogram-Estimated Mutual Information with the Target

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 Median of Slippage

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 Anomaly Flag

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

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)

Percent-Change from a Configurable Base

Quantile Estimate from Pre-Bucketed Histogram Counts

Linear-Interpolation Percentile of Trade PnL

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

Long-to-Wide Pivot — Reshape a (Date, Ticker, Value) Panel into a Matrix

Aggregate P&L Up a Portfolio Hierarchy Tree

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

Probability of Reaching a Target Leaf Set on a Binary Scenario Tree

Purged k-Fold CV with Embargo

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

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

Spearman Rank Correlation with Average-Rank Tie Breaking

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)

Recursive Walk Down a Hierarchical Rebate-Tier Tree

Per-Node Conditional Expected Leaf Payoff on a Scenario Tree

Regime-Conditional Historical Expected Shortfall

Regime-Conditional Historical VaR

Regime Transition Path Count: Modular DAG Walk Enumeration with Distinguishable Catalysts

Resample Tick Prints into Fixed-Interval OHLC Bars

Reverse Stress Test — Flag Scenarios That Hit a Loss Target

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

Rolling Beta — Strategy vs. Benchmark

Rolling Beta vs Benchmark

Rolling Engle-Granger Cointegration Test for Pairs Trading

Rolling Pearson Correlation Between Two Series

Rolling Max-Min Spread

Longest Stable-Volatility Regime via Rolling Sample-Stddev Sliding Window

Minute-Bar Range Monitor via Dual-Deque Sliding Max-Minus-Min

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

Expected PnL on a Risk-Officer Scenario Tree

Worst-Case Leaf PnL on a Risk-Officer Scenario Tree

Semi-Deviation of a Return Series Around the Sample Mean

Shortest Window Containing K Magnitude Spikes in a Return Stream

Toy Ledoit-Wolf Shrinkage Covariance

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

Size-Weighted Median Fill Price

Annualized Sortino Ratio

Spectral Risk Measure (Acerbi 2002)

European Call MC with Stratified Sampling on Terminal Z

Stress Coverage Ratios Against Available Capital

Stress-Loss Aggregation by Bucket

Stressed Expected Shortfall — Worst Rolling-Window Historical ES

Stressed VaR — Worst Rolling-Window Historical VaR

Subranges Above Return Threshold

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

T-Digest Streaming Percentile Estimator (k_1 Scale Function)

Top K PnL Days So Far

Search a Binary Search Tree for a Target

Validate Binary Search Tree (Recursive Bounds)

Lag-1 Autocorrelation of VaR Hit Indicators

Vasicek Single-Factor Conditional PD Given a Realized Systematic Factor

Vasicek MLE Fit from a Short-Rate Series

VWAP Deviation by Broker

Walk-Forward Train/Test Splits with Embargo

Walk-forward CV: Expanding and Rolling-window Folds

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

Rolling Hit-Rate of Strictly-Positive Returns over a Fixed-Size Window

Cross-Sectional Winsorization of Alpha-Factor Values

Cross-Sectional Z-Score with Optional Winsorization