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Almgren-Chriss Static Optimal Execution Trajectory

Shrinkage Blend of Two Alpha Sources with Z-Score Normalization

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

Antithetic Variates Variance Reduction

Arrival Price vs TWAP Decision under Alpha Decay

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

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

As-of Merge — Trades against Quotes

Per-Asset Beta to a Benchmark Portfolio

Bachelier (Normal) Implied Vol from a Quoted Call

Credit-Based Backpressure — Replay Producer/Consumer Events into a State Trace

Daily Backtest with Overnight Borrow Cost

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

Basel IRB Risk-Weighted Asset for a Corporate Exposure

Basel VaR Backtest Traffic-Light Zones

Bermudan Put on a CRR Tree with Selective Early-Exercise

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

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

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

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

Discrete Bucket-Vega Hedge Allocator

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

Calmar Ratio — Annualized Return over Maximum Drawdown

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

Implied Default Probability from a CDS Spread

Choueifaty Diversification Ratio of a Gaussian Portfolio

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

Compact a Ring-Buffer of Ticks into Evenly-Bucketed Time Slices

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

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 Portfolio Expected Loss and Naive Unexpected Loss

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

Cross-Gamma PnL Attribution: Two-Asset Greek Decomposition

Cross-Sectional Demean of an Alpha Factor

Rank-to-Percentile Transform on a Cross-Section of Alpha Factors

DAG Multi-Worker Topological Schedule

DAG Schedule on K Machines with Critical-Path Priority

Decile-Spread Forward Return Averaged Across Dates

Deduplicate a Replayed Tick Stream by (ts, exchange-seq), Latest-Ingest Wins

Bump-and-Revalue Finite-Difference Delta

Discrete Delta-Hedge Path Simulation with Transaction Costs

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

Divide-and-Conquer Sum Tree (Parallel Reduction Simulation)

Dollar Gamma Across a Strike Ladder

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

Downsample a Tick Stream into OHLCV Bars (Right-Closed)

Weighted Edit Distance with Per-Character Cost Matrices

Empirical Copula via Per-Column Uniform Rank Transform

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)

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

EWMA Volatility Update

Excess Returns Over a Benchmark

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

Optimal Execution Trajectory Under Hard Per-Bucket Volume Caps

Rolling Historical Expected Shortfall (CVaR)

Expected Value at Root of Scenario Tree

Per-Factor Risk Attribution Under a Linear Factor Model

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

Fan-Out / Fan-In Coordination — Event Replay

Per-Venue Fill Rate with Wilson Confidence Intervals

OU First-Passage Time by Monte Carlo

Fixed-strike Lookback Call MC Pricing with Discrete Monitoring

Pricing a Floating-Rate Note from a Zero Curve

Fork-Join Segment Stats (Welford Pairwise Merge)

Forward-Fill Missing Minutes Within a Trading Session

Cross-Hedge Residual Variance and Explanatory Power

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

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

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 Stress Loss Replay

Historical VaR for a Long-Only Portfolio

Rolling Historical VaR Track

IC-Weighted Alpha Signal Combination

Iceberg Order Book — Replenishment & Fills

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

Jarrow-Rudd Binomial Tree for European Options

Merton Jump-Diffusion European Call via Monte Carlo

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

Kupiec Proportion-of-Failures (POF) Test Statistic

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

Basel III Liquidity Coverage Ratio with HQLA Caps

Leaky-Bucket Rate Limiter as Admission Control

Leisen-Reimer Binomial Tree for European Options

Basel III Leverage Ratio

LGD Aggregation with Collateral Recovery Cascade

Limit-Order Fill Simulation against High-Low Bars

Linear Market-Impact Cost of a Child-Order Schedule

Look-Ahead Bias Detector via Lagged-Correlation Comparison

Fixed-Strike Lookback Call Pricing via Monte Carlo

Robust Cross-Sectional Z-Score via Median and MAD

MapReduce Group-By Count (Two-Phase Aggregation)

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

Mean-Reversion Factor — Residualized Last-K Return

Long-Only Mean-Variance Efficient Frontier

Merge Per-Day Bar Shards into a Sorted Timeseries

Two-Asset Minimum-Variance Portfolio (Closed Form)

Long-Only Minimum-Variance Portfolio Weights

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

Monte-Carlo VaR for a Multi-Asset Portfolio

Multi-Leg Implementation Shortfall — Basket Covariance Attribution

Multi-Level Monte Carlo for a European Call

Multi-Period DP for Optimal Execution Under Impact and Risk

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

Rank Features by Histogram-Estimated Mutual Information with the Target

Group-Neutralize a Factor by Sector Tag

Basel III Net Stable Funding Ratio (NSFR)

Omega Ratio of a Return Series at a Threshold

Online PCA via Oja's Rule (Streaming PC1)

Online Z-Score Anomaly Flag

Classical Gram-Schmidt Orthogonalization of Priority-Ordered Alpha Signals

Parallel Pairwise Mean Merge with Kahan Compensation

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

Post-Earnings Announcement Drift Signal (D+1 to D+60 Excess Return)

Percent-Change from a Configurable Base

Quantile Estimate from Pre-Bucketed Histogram Counts

Cache-Aware Pipeline Replay — Minimum Re-run Set with Input-Hash Chaining

Research Pipeline DAG — Cascade-Invalidate Downstream of a Failed Task

Research Pipeline DAG — Compute the Next-Runnable Set

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

Greek-Based PnL Attribution

Greek-Attribution P&L Explain with Residual Diagnostic

Aggregate Book Delta per Underlying

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

Per-Asset and Portfolio Cap Clamping for Target Weights

Position P&L With Transaction Fees

Reactive POV Schedule with Min/Max Catch-Up Bounds

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

Price-Time Priority Queue — Order Book Replay

Priority-Driven Task Scheduling with Deps on a Worker Pool

Pro-Rata Allocation — Single-Level Fill Distribution

Prune Binomial Tree to Min Nodes

Purged k-Fold CV with Embargo

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

Queue Position Fill Probability — Closed-Form Under Poisson Arrivals

Quintile (k-tile) Bucketing of a Cross-Sectional Factor

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

Cross-Sectional Rank Bucketing into Deciles with Ordinal Tie-Breaks

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

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

Turnover-Aware Rebalance on Bucketed-Signal Change

Sparse Vanilla Replication of an Exotic Payoff

Resample Tick Prints into Fixed-Interval OHLC Bars

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 Max-Min Spread

Rolling-Window Variance Ratio Test (Lo-MacKinlay)

Rolling Z-Score Anomaly Flags

Hagan SABR Implied Lognormal Vol from Parameters

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

Sector-Neutralize an Alpha Factor Cross-Section

Semi-Deviation of a Return Series Around the Sample Mean

Session-Window Aggregation — Gap-Driven Boundaries

Implementation Shortfall — Fee vs Market-Impact Decomposition

Toy Ledoit-Wolf Shrinkage Covariance

Multi-Horizon Signal Blend with Time Decay

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

Sliding-Window Mean — Fixed-Count Window with O(1) Eviction

Sliding-Log Rate Limiter (Deque of Admitted Timestamps)

Multi-Level SOR with Stale-Quote Re-Routing — Event Replay

Min-Venue-Count Smart Order Routing with Fee-Tier Crossing Penalty

SOR Across Replenishing Iceberg Venues — Event Replay

Fee-Aware Static Smart-Order Routing Across Venues

Smart-Order Routing With Bayesian Fill-Rate Priors and UCB Exploration

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-Loss Aggregation by Bucket

Survivorship-Aware Tradeable Universe on a Date

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)

Target-Volatility Scaling with Leverage Cap

T-Digest Streaming Percentile Estimator (k_1 Scale Function)

Multi-Position Four-Greek P&L Attribution with Theta Decay

Tick Buffer — Binary-Search Lookup and Range Scan by Timestamp

Token-Bucket Rate Limiter with Bounded Pending Queue

Equal-Weight Long-Top-K / Short-Bottom-K Portfolio

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

Tree Reduction with (min, max) Associative Combiner

Treynor Ratio — Systematic-Risk-Adjusted Excess Return

Boyle Trinomial Tree for an American Put

CRR3 Trinomial Tree for a European Call

Tumbling-Window Aggregation — Sparse Per-Bucket Stats

Turnover-Constrained Portfolio Rebalance

TWAP Equal-Slice Schedule with Front-Loaded Residue

TWAP Scheduling Through Forbidden No-Go Windows

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

Up-Capture and Down-Capture Ratios versus a Benchmark

Count and Timestamp VaR Breaches

Vasicek ASRF Loss Rate

Vasicek MLE Fit from a Short-Rate Series

Vasicek Short-Rate MLE Calibration on a Historical Series

Vectorized PnL with Time-Varying Borrow Fee Curve

Vectorized Per-Period PnL with Transaction Costs

Bucket Vega Exposure by Maturity

Vega-Bucketed PnL Explain Across a Strike Grid

Static Vega Replication of an Exotic into a Vanilla Basis

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

VWAP Tracking-Error P&L

VWAP Schedule Along a Volume Curve with Participation Cap

Walk-Forward Train/Test Splits with Embargo

Walk-forward CV: Expanding and Rolling-window Folds

Walk-Forward Validation for Time-Series Backtests

Watermark-Driven Tumbling Windows with Late-Event Handling

Welford's Online Variance

Tumbling Window Trigger Firing Policies (Early, On-Close, Speculative)

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