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Refactor code structure for improved readability and maintainability
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# Implied Volatility Prediction from Options Data
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[](https://www.r-project.org/)
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[]()
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[]()
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> **M2 Master's Project** – Predicting implied volatility using advanced regression techniques and machine learning models on financial options data.
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This project explores the prediction of **implied volatility** from options market data, combining classical statistical methods with modern machine learning approaches. The analysis covers data preprocessing, feature engineering, model benchmarking, and interpretability analysis using real-world financial panel data.
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---
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## 📋 Project Overview
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### Problem Statement
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Implied volatility represents the market's forward-looking expectation of an asset's future volatility. Accurate prediction is crucial for:
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- **Option pricing** and valuation
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- **Risk management** and hedging strategies
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- **Trading strategies** based on volatility arbitrage
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### Dataset
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The project uses a comprehensive panel dataset tracking **3,887 assets** across **544 observation dates** (2019-2022):
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| File | Description | Shape |
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|------|-------------|-------|
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| `Train_ISF.csv` | Training data with target variable | 1,909,465 rows × 21 columns |
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| `Test_ISF.csv` | Test data for prediction | 1,251,308 rows × 18 columns |
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| `hat_y.csv` | Final predictions from both models | 1,251,308 rows × 2 columns |
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### Key Variables
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**Target Variable:**
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- `implied_vol_ref` – The implied volatility to predict
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**Feature Categories:**
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- **Identifiers:** `asset_id`, `obs_date`
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- **Market Activity:** `call_volume`, `put_volume`, `call_oi`, `put_oi`, `total_contracts`
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- **Volatility Metrics:** `realized_vol_short`, `realized_vol_mid1-3`, `realized_vol_long1-4`, `market_vol_index`
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- **Option Structure:** `strike_dispersion`, `maturity_count`
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---
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## 🏗️ Methodology
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### Data Pipeline
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```
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Raw Data
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↓
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┌─────────────────────────────────────────────────────────┐
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│ Data Splitting (Chronological 80/20) │
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│ - Training: 2019-10 to 2021-07 │
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│ - Validation: 2021-07 to 2022-03 │
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└─────────────────────────────────────────────────────────┘
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↓
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┌─────────────────────────────────────────────────────────┐
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│ Feature Engineering │
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│ - Aggregation of volatility horizons │
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│ - Creation of financial indicators │
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└─────────────────────────────────────────────────────────┘
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↓
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┌─────────────────────────────────────────────────────────┐
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│ Data Preprocessing (tidymodels) │
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│ - Winsorization (99.5th percentile) │
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│ - Log/Yeo-Johnson transformations │
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│ - Z-score normalization │
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│ - PCA (95% variance retention) │
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└─────────────────────────────────────────────────────────┘
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↓
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Three Datasets Generated:
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├── Tree-based (raw, scale-invariant)
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├── Linear (normalized, winsorized)
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└── PCA (dimensionality-reduced)
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```
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### Feature Engineering
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New financial indicators created to capture market dynamics:
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| Feature | Description | Formula |
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|---------|-------------|---------|
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| `pulse_ratio` | Volatility trend direction | RV_short / RV_long |
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| `stress_spread` | Asset vs market stress | RV_short - Market_VIX |
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| `put_call_ratio_volume` | Immediate market stress | Put_Volume / Call_Volume |
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| `put_call_ratio_oi` | Long-term risk structure | Put_OI / Call_OI |
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| `liquidity_ratio` | Market depth | Total_Volume / Total_OI |
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| `option_dispersion` | Market uncertainty | Strike_Dispersion / Total_Contracts |
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| `put_low_strike` | Downside protection density | Strike_Dispersion / Put_OI |
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| `put_proportion` | Hedging vs speculation | Put_Volume / Total_Volume |
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---
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## 🤖 Models Implemented
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### Linear Models
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| Model | Description | Best RMSE |
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|-------|-------------|-----------|
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| **OLS** | Ordinary Least Squares | 11.26 |
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| **Ridge** | L2 regularization | 12.48 |
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| **Lasso** | L1 regularization (variable selection) | 12.03 |
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| **Elastic Net** | L1 + L2 combined | ~12.03 |
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| **PLS** | Partial Least Squares (on PCA) | 12.79 |
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### Linear Mixed-Effects Models (LMM)
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Advanced panel data models accounting for asset-specific effects:
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| Model | Features | RMSE |
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|-------|----------|------|
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| LMM Baseline | All variables + Random Intercept | 8.77 |
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| LMM Reduced | Collinearity removal | ~8.77 |
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| LMM Interactions | Financial interaction terms | ~8.77 |
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| LMM + Quadratic | Convexity terms (vol of vol) | 8.41 |
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| **LMM + Random Slopes (mod_lmm_5)** | Asset-specific betas | **8.10** ⭐ |
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### Tree-Based Models
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| Model | Strategy | Validation RMSE | Training RMSE |
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|-------|----------|-----------------|---------------|
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| **XGBoost** | Level-wise, Bayesian tuning | 10.70 | 0.57 |
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| **LightGBM** | Leaf-wise, feature regularization | **10.61** ⭐ | 10.90 |
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| Random Forest | Bagging | DNF* | - |
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*DNF: Did Not Finish (computational constraints)
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### Neural Networks
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| Model | Architecture | Status |
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|-------|--------------|--------|
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| MLP | 128-64 units, tanh activation | Failed to converge |
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---
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## 📊 Results Summary
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### Model Comparison
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```
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RMSE Performance (Lower is Better)
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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Linear Mixed-Effects (LMM5) 8.38 ████████████████████ Best Linear
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Linear Mixed-Effects (LMM4) 8.41 ███████████████████
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Linear Mixed-Effects (Baseline) 8.77 ██████████████████
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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LightGBM 10.61 ███████████████ Best Non-Linear
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XGBoost 10.70 ██████████████
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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OLS (with interactions) 11.26 █████████████
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Lasso 12.03 ███████████
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OLS (baseline) 12.01 ███████████
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Ridge 12.48 ██████████
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PLS 12.79 █████████
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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```
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### Key Findings
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1. **Best Linear Model:** LMM with Random Slopes (RMSE = 8.38)
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- Captures asset-specific volatility sensitivities
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- Includes quadratic terms for convexity effects
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2. **Best Non-Linear Model:** LightGBM (RMSE = 10.61)
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- Superior generalization vs XGBoost
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- Feature regularization prevents overfitting
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3. **Interpretability Insights (SHAP Analysis):**
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- `realized_vol_mid` dominates (57% of gain)
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- Volatility clustering confirmed as primary driver
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- Non-linear regime switching in stress_spread
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---
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## 📁 Repository Structure
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```
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PROJECT/
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├── Projet_MRC_DANJOU_LEGRAND_MERIC_VONSIEMENS.qmd # Main analysis (Quarto)
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├── Projet_MRC_DANJOU_LEGRAND_MERIC_VONSIEMENS.html # Rendered report
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├── packages.R # R dependencies installer
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├── Train_ISF.csv # Training data (~1.9M rows)
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├── Test_ISF.csv # Test data (~1.25M rows)
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├── hat_y.csv # Final predictions
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├── README.md # This file
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└── results/
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├── lightgbm/ # LightGBM model outputs
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└── xgboost/ # XGBoost model outputs
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```
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---
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## 🚀 Getting Started
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### Prerequisites
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- **R** ≥ 4.0
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- Required packages (auto-installed via `packages.R`)
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### Installation
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```r
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# Install all dependencies
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source("packages.R")
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```
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Or manually install key packages:
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```r
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install.packages(c(
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"tidyverse", "tidymodels", "caret", "glmnet",
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"lme4", "lmerTest", "xgboost", "lightgbm",
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"ranger", "pls", "shapviz", "rBayesianOptimization"
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))
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```
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### Running the Analysis
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1. **Open the Quarto document:**
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```r
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# In RStudio
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rstudioapi::navigateToFile("Projet_MRC_DANJOU_LEGRAND_MERIC_VONSIEMENS.qmd")
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```
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2. **Render the document:**
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```r
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quarto::quarto_render("Projet_MRC_DANJOU_LEGRAND_MERIC_VONSIEMENS.qmd")
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```
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3. **Or run specific sections interactively** using the code chunks in the `.qmd` file
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---
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## 🛠️ Technical Details
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### Data Split Strategy
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- **Chronological split** at 80th percentile of dates
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- Prevents look-ahead bias and data leakage
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- Training: ~1.53M observations
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- Validation: ~376K observations
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### Hyperparameter Tuning
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- **Method:** Bayesian Optimization (Gaussian Processes)
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- **Acquisition:** Expected Improvement (UCB)
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- **Goal:** Maximize negative RMSE
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### Evaluation Metric
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**Exponential RMSE** on original scale:
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$$
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RMSE_{real} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} \left( \exp(\hat{y}_{\log, i}) - y_i \right)^2}
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$$
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Models trained on log-transformed target for variance stabilization.
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---
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## 📖 Key Concepts
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### Financial Theories Applied
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1. **Volatility Clustering** – Past volatility predicts future volatility
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2. **Variance Risk Premium** – Spread between implied and realized volatility
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3. **Fear Gauge** – Put-call ratio as sentiment indicator
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4. **Mean Reversion** – Volatility tends to return to long-term average
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5. **Liquidity Premium** – Illiquid assets command higher volatility
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### Statistical Methods
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- Panel data modeling with fixed and random effects
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- Principal Component Analysis (PCA)
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- Bayesian hyperparameter optimization
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- SHAP values for model interpretability
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---
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## 👥 Authors
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**Team:**
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- Arthur DANJOU
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- Camille LEGRAND
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- Axelle MERIC
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- Moritz VON SIEMENS
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**Course:** Classification and Regression (M2)
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**Academic Year:** 2025-2026
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---
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## 📝 Notes
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- **Computational Constraints:** Some models (Random Forest, MLP) failed due to hardware limitations (16GB RAM, CPU-only)
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- **Reproducibility:** Set `seed = 2025` for consistent results
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- **Language:** Analysis documented in English, course materials in French
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---
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## 📚 References
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Key R packages used:
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- `tidymodels` – Modern modeling framework
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- `glmnet` – Regularized regression
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- `lme4` / `lmerTest` – Mixed-effects models
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- `xgboost` / `lightgbm` – Gradient boosting
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- `shapviz` – Model interpretability
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- `rBayesianOptimization` – Hyperparameter tuning
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# Liste des packages nécessaires
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packages <- c(
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"tidyverse",
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"rsample",
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"scales",
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"dplyr",
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"tidyr",
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"glue",
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"corrplot",
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"ggfortify",
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"carData",
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"car",
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"MASS",
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"ggplot2",
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"DataExplorer",
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"skimr",
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"plotly",
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"gridExtra",
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"grid",
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"rlang",
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"caret",
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"reshape2",
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"class",
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"ROCR",
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"randomForest",
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"fitdistrplus",
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"hexbin",
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"paletteer"
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)
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# Fonction pour installer les packages manquants
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install_if_missing <- function(p) {
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if (!require(p, character.only = TRUE)) {
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install.packages(p, dependencies = TRUE)
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}
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}
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# Application de la fonction sur toute la liste
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invisible(sapply(packages, install_if_missing))
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# Chargement de toutes les librairies
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invisible(lapply(packages, library, character.only = TRUE))
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message("Tous les packages ont été installés et chargés avec succès !")
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# RL Project: Atari Tennis Tournament
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Comparison of Reinforcement Learning algorithms on Atari Tennis (`ALE/Tennis-v5` via Gymnasium/PettingZoo).
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|
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## Overview
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This project implements and compares five RL agents playing Atari Tennis against the built-in AI and in head-to-head tournaments.
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## Algorithms
|
||||
|
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| Agent | Type | Policy | Update Rule |
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|-------|------|--------|-------------|
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| **Random** | Baseline | Uniform random | None |
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| **SARSA** | TD(0), on-policy | ε-greedy | $W_a \leftarrow W_a + \alpha \cdot (r + \gamma \hat{q}(s', a') - \hat{q}(s, a)) \cdot \phi(s)$ |
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| **Q-Learning** | TD(0), off-policy | ε-greedy | $W_a \leftarrow W_a + \alpha \cdot (r + \gamma \max_{a'} \hat{q}(s', a') - \hat{q}(s, a)) \cdot \phi(s)$ |
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| **Monte Carlo** | First-visit MC | ε-greedy | $W_a \leftarrow W_a + \alpha \cdot (G_t - \hat{q}(s, a)) \cdot \phi(s)$ |
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| **DQN** | Deep Q-Network | ε-greedy | MLP (256→256) with experience replay & target network |
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|
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## Architecture
|
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|
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- **Linear agents** (SARSA, Q-Learning, Monte Carlo): $\hat{q}(s, a; \mathbf{W}) = \mathbf{W}_a^\top \phi(s)$ with $\phi(s) \in \mathbb{R}^{128}$ (RAM observation)
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||||
- **DQN**: MLP network (128 → 128 → 64 → 18) trained with Adam optimizer, Huber loss, and periodic target network sync
|
||||
|
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## Environment
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||||
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- **Game**: Atari Tennis via PettingZoo (`tennis_v3`)
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- **Observation**: RAM state (128 features)
|
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- **Action Space**: 18 discrete actions
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- **Agents**: 2 players (`first_0` and `second_0`)
|
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|
||||
## Project Structure
|
||||
|
||||
```
|
||||
.
|
||||
├── Project_RL_DANJOU_VON-SIEMENS.ipynb # Main notebook
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├── README.md # This file
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||||
├── checkpoints/ # Saved agent weights
|
||||
│ ├── sarsa.pkl
|
||||
│ ├── q_learning.pkl
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│ ├── montecarlo.pkl
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||||
│ └── dqn.pkl
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└── plots/ # Training & evaluation plots
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||||
├── SARSA_training_curves.png
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||||
├── Q-Learning_training_curves.png
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||||
├── MonteCarlo_training_curves.png
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||||
├── DQN_training_curves.png
|
||||
├── evaluation_results.png
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||||
└── championship_matrix.png
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||||
```
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|
||||
## Key Results
|
||||
|
||||
### Win Rate vs Random Baseline
|
||||
|
||||
| Agent | Win Rate |
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|-------|----------|
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| SARSA | 88.9% |
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| Q-Learning | 41.2% |
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||||
| Monte Carlo | 47.1% |
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||||
| DQN | 6.2% |
|
||||
|
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### Championship Tournament
|
||||
|
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Full round-robin tournament where each agent faces every other agent in both positions (first_0/second_0).
|
||||
|
||||
## Notebook Sections
|
||||
|
||||
1. **Configuration & Checkpoints** — Incremental training workflow with pickle serialization
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||||
2. **Utility Functions** — Observation normalization, ε-greedy policy
|
||||
3. **Agent Definitions** — `RandomAgent`, `SarsaAgent`, `QLearningAgent`, `MonteCarloAgent`, `DQNAgent`
|
||||
4. **Training Infrastructure** — `train_agent()`, `plot_training_curves()`
|
||||
5. **Evaluation** — Match system, random baseline, round-robin tournament
|
||||
6. **Results & Visualization** — Win rate plots, matchup matrix heatmap
|
||||
|
||||
## Known Issues
|
||||
|
||||
- **Monte Carlo & DQN**: Checkpoint loading issues — saved weights may not restore properly during evaluation (training works correctly)
|
||||
|
||||
## Dependencies
|
||||
|
||||
- Python 3.13+
|
||||
- `numpy`, `matplotlib`
|
||||
- `torch`
|
||||
- `gymnasium`, `ale-py`
|
||||
- `pettingzoo`
|
||||
- `tqdm`
|
||||
|
||||
## Authors
|
||||
|
||||
- Arthur DANJOU
|
||||
- Moritz VON SIEMENS
|
||||
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@@ -37,7 +37,6 @@
|
||||
| Course | Description |
|
||||
|--------|-------------|
|
||||
| `Advanced Machine Learning` | Advanced ML techniques |
|
||||
| `Classification and Regression` | Supervised learning methods |
|
||||
| `Clustering In Practice` | Unsupervised learning and clustering |
|
||||
| `Data Visualisation` | Data visualization principles and tools |
|
||||
| `Deep Learning` | Neural networks and deep architectures |
|
||||
@@ -51,7 +50,6 @@
|
||||
| `Statistiques Non Paramétrique` | Non-parametric statistics |
|
||||
| `Time Series` | Time series analysis and forecasting |
|
||||
| `Unsupervised Learning` | Unsupervised learning methods |
|
||||
| `VBA` | Visual Basic for Applications |
|
||||
|
||||
## 🛠️ Technologies & Tools
|
||||
|
||||
|
||||
@@ -5,34 +5,31 @@ description = "A curated collection of mathematics and data science projects dev
|
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readme = "README.md"
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# "sequenzo>=0.1.20",
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352
uv.lock
generated
352
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[[package]]
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{ url = "https://files.pythonhosted.org/packages/5e/49/4971affd9c62d26b3ff4a84dc6432275be72d9615d95f7bb9e027beeeed8/uv-0.10.9-py3-none-win_arm64.whl", hash = "sha256:47e18a0521d76293d4f60d129f520b18bddf1976b4a47b50f0fcb04fb6a9d40f", size = 22454171, upload-time = "2026-03-06T21:21:24.596Z" },
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]
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[[package]]
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@@ -3149,18 +2991,6 @@ wheels = [
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{ url = "https://files.pythonhosted.org/packages/a4/74/a148b41572656904a39dfcfed3f84dd1066014eed94e209223ae8e9d088d/weasel-0.4.3-py3-none-any.whl", hash = "sha256:08f65b5d0dbded4879e08a64882de9b9514753d9eaa4c4e2a576e33666ac12cf", size = 50757, upload-time = "2025-11-13T23:52:26.982Z" },
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]
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[[package]]
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name = "werkzeug"
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version = "3.1.6"
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source = { registry = "https://pypi.org/simple" }
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dependencies = [
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{ name = "markupsafe" },
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]
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sdist = { url = "https://files.pythonhosted.org/packages/61/f1/ee81806690a87dab5f5653c1f146c92bc066d7f4cebc603ef88eb9e13957/werkzeug-3.1.6.tar.gz", hash = "sha256:210c6bede5a420a913956b4791a7f4d6843a43b6fcee4dfa08a65e93007d0d25", size = 864736, upload-time = "2026-02-19T15:17:18.884Z" }
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wheels = [
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{ url = "https://files.pythonhosted.org/packages/4d/ec/d58832f89ede95652fd01f4f24236af7d32b70cab2196dfcc2d2fd13c5c2/werkzeug-3.1.6-py3-none-any.whl", hash = "sha256:7ddf3357bb9564e407607f988f683d72038551200c704012bb9a4c523d42f131", size = 225166, upload-time = "2026-02-19T15:17:17.475Z" },
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]
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[[package]]
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||||
name = "wheel"
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version = "0.46.3"
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||||
|
||||
Reference in New Issue
Block a user