[{"data":1,"prerenderedAt":1881},["ShallowReactive",2],{"project-implied-volatility-prediction-from-options-data":3},{"id":4,"title":5,"description":6,"extension":7,"favorite":8,"icon":9,"meta":10,"publishedAt":1869,"readingTime":824,"shortDescription":1870,"slug":1871,"status":1872,"stem":1873,"tags":1874,"type":1879,"__hash__":1880},"projects\u002Fprojects\u002Fglm-implied-volatility.md","Implied Volatility Prediction from Options Data","A large-scale statistical study comparing Generalized Linear Models (GLMs) and black-box machine learning architectures to predict the implied volatility of S&P 500 options.","md",false,"i-ph-graph-duotone",{"body":11},{"type":12,"value":13,"toc":1830},"minimark",[14,25,32,49,52,57,62,65,85,89,100,163,167,172,180,185,247,249,253,257,267,271,274,394,396,400,404,485,489,492,567,571,638,641,645,672,674,678,682,688,692,742,744,748,754,756,760,764,779,783,804,807,840,844,890,892,896,900,917,921,941,945,951,1644,1647,1649,1653,1657,1689,1693,1707,1709,1713,1718,1732,1742,1744,1748,1772,1774,1778,1781,1826],[15,16,17],"blockquote",{},[18,19,20,24],"p",{},[21,22,23],"strong",{},"M2 Master's Project"," – Predicting implied volatility using advanced regression techniques and machine learning models on financial options data.",[18,26,27,28,31],{},"This project explores the prediction of ",[21,29,30],{},"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.",[33,34,35],"ul",{},[36,37,38,41,42],"li",{},[21,39,40],{},"GitHub Repository:"," ",[43,44,48],"a",{"href":45,"rel":46},"https:\u002F\u002Fgithub.com\u002FArthurDanjou\u002FImplied-Volatility-from-Options-Data",[47],"nofollow","Implied-Volatility-from-Options-Data",[50,51],"hr",{},[53,54,56],"h2",{"id":55},"project-overview","Project Overview",[58,59,61],"h3",{"id":60},"problem-statement","Problem Statement",[18,63,64],{},"Implied volatility represents the market's forward-looking expectation of an asset's future volatility. Accurate prediction is crucial for:",[33,66,67,73,79],{},[36,68,69,72],{},[21,70,71],{},"Option pricing"," and valuation",[36,74,75,78],{},[21,76,77],{},"Risk management"," and hedging strategies",[36,80,81,84],{},[21,82,83],{},"Trading strategies"," based on volatility arbitrage",[58,86,88],{"id":87},"dataset","Dataset",[18,90,91,92,95,96,99],{},"The project uses a comprehensive panel dataset tracking ",[21,93,94],{},"3,887 assets"," across ",[21,97,98],{},"544 observation dates"," (2019-2022):",[101,102,103,119],"table",{},[104,105,106],"thead",{},[107,108,109,113,116],"tr",{},[110,111,112],"th",{},"File",[110,114,115],{},"Description",[110,117,118],{},"Shape",[120,121,122,137,150],"tbody",{},[107,123,124,131,134],{},[125,126,127],"td",{},[128,129,130],"code",{},"Train_ISF.csv",[125,132,133],{},"Training data with target variable",[125,135,136],{},"1,909,465 rows × 21 columns",[107,138,139,144,147],{},[125,140,141],{},[128,142,143],{},"Test_ISF.csv",[125,145,146],{},"Test data for prediction",[125,148,149],{},"1,251,308 rows × 18 columns",[107,151,152,157,160],{},[125,153,154],{},[128,155,156],{},"hat_y.csv",[125,158,159],{},"Final predictions from both models",[125,161,162],{},"1,251,308 rows × 2 columns",[58,164,166],{"id":165},"key-variables","Key Variables",[18,168,169],{},[21,170,171],{},"Target Variable:",[33,173,174],{},[36,175,176,179],{},[128,177,178],{},"implied_vol_ref"," – The implied volatility to predict",[18,181,182],{},[21,183,184],{},"Feature Categories:",[33,186,187,199,219,236],{},[36,188,189,41,192,195,196],{},[21,190,191],{},"Identifiers:",[128,193,194],{},"asset_id",", ",[128,197,198],{},"obs_date",[36,200,201,41,204,195,207,195,210,195,213,195,216],{},[21,202,203],{},"Market Activity:",[128,205,206],{},"call_volume",[128,208,209],{},"put_volume",[128,211,212],{},"call_oi",[128,214,215],{},"put_oi",[128,217,218],{},"total_contracts",[36,220,221,41,224,195,227,195,230,195,233],{},[21,222,223],{},"Volatility Metrics:",[128,225,226],{},"realized_vol_short",[128,228,229],{},"realized_vol_mid1-3",[128,231,232],{},"realized_vol_long1-4",[128,234,235],{},"market_vol_index",[36,237,238,41,241,195,244],{},[21,239,240],{},"Option Structure:",[128,242,243],{},"strike_dispersion",[128,245,246],{},"maturity_count",[50,248],{},[53,250,252],{"id":251},"methodology","Methodology",[58,254,256],{"id":255},"data-pipeline","Data Pipeline",[258,259,264],"pre",{"className":260,"code":262,"language":263},[261],"language-text","Raw Data\n    ↓\n┌─────────────────────────────────────────────────────────┐\n│  Data Splitting (Chronological 80\u002F20)                   │\n│  - Training: 2019-10 to 2021-07                         │\n│  - Validation: 2021-07 to 2022-03                       │\n└─────────────────────────────────────────────────────────┘\n    ↓\n┌─────────────────────────────────────────────────────────┐\n│  Feature Engineering                                    │\n│  - Aggregation of volatility horizons                   │\n│  - Creation of financial indicators                     │\n└─────────────────────────────────────────────────────────┘\n    ↓\n┌─────────────────────────────────────────────────────────┐\n│  Data Preprocessing (tidymodels)                        │\n│  - Winsorization (99.5th percentile)                    │\n│  - Log\u002FYeo-Johnson transformations                      │\n│  - Z-score normalization                                │\n│  - PCA (95% variance retention)                         │\n└─────────────────────────────────────────────────────────┘\n    ↓\nThree Datasets Generated:\n├── Tree-based (raw, scale-invariant)\n├── Linear (normalized, winsorized)\n└── PCA (dimensionality-reduced)\n","text",[128,265,262],{"__ignoreMap":266},"",[58,268,270],{"id":269},"feature-engineering","Feature Engineering",[18,272,273],{},"New financial indicators created to capture market dynamics:",[101,275,276,288],{},[104,277,278],{},[107,279,280,283,285],{},[110,281,282],{},"Feature",[110,284,115],{},[110,286,287],{},"Formula",[120,289,290,303,316,329,342,355,368,381],{},[107,291,292,297,300],{},[125,293,294],{},[128,295,296],{},"pulse_ratio",[125,298,299],{},"Volatility trend direction",[125,301,302],{},"RV_short \u002F RV_long",[107,304,305,310,313],{},[125,306,307],{},[128,308,309],{},"stress_spread",[125,311,312],{},"Asset vs market stress",[125,314,315],{},"RV_short - Market_VIX",[107,317,318,323,326],{},[125,319,320],{},[128,321,322],{},"put_call_ratio_volume",[125,324,325],{},"Immediate market stress",[125,327,328],{},"Put_Volume \u002F Call_Volume",[107,330,331,336,339],{},[125,332,333],{},[128,334,335],{},"put_call_ratio_oi",[125,337,338],{},"Long-term risk structure",[125,340,341],{},"Put_OI \u002F Call_OI",[107,343,344,349,352],{},[125,345,346],{},[128,347,348],{},"liquidity_ratio",[125,350,351],{},"Market depth",[125,353,354],{},"Total_Volume \u002F Total_OI",[107,356,357,362,365],{},[125,358,359],{},[128,360,361],{},"option_dispersion",[125,363,364],{},"Market uncertainty",[125,366,367],{},"Strike_Dispersion \u002F Total_Contracts",[107,369,370,375,378],{},[125,371,372],{},[128,373,374],{},"put_low_strike",[125,376,377],{},"Downside protection density",[125,379,380],{},"Strike_Dispersion \u002F Put_OI",[107,382,383,388,391],{},[125,384,385],{},[128,386,387],{},"put_proportion",[125,389,390],{},"Hedging vs speculation",[125,392,393],{},"Put_Volume \u002F Total_Volume",[50,395],{},[53,397,399],{"id":398},"models-implemented","Models Implemented",[58,401,403],{"id":402},"linear-models","Linear Models",[101,405,406,418],{},[104,407,408],{},[107,409,410,413,415],{},[110,411,412],{},"Model",[110,414,115],{},[110,416,417],{},"Best RMSE",[120,419,420,433,446,459,472],{},[107,421,422,427,430],{},[125,423,424],{},[21,425,426],{},"OLS",[125,428,429],{},"Ordinary Least Squares",[125,431,432],{},"11.26",[107,434,435,440,443],{},[125,436,437],{},[21,438,439],{},"Ridge",[125,441,442],{},"L2 regularization",[125,444,445],{},"12.48",[107,447,448,453,456],{},[125,449,450],{},[21,451,452],{},"Lasso",[125,454,455],{},"L1 regularization (variable selection)",[125,457,458],{},"12.03",[107,460,461,466,469],{},[125,462,463],{},[21,464,465],{},"Elastic Net",[125,467,468],{},"L1 + L2 combined",[125,470,471],{},"~12.03",[107,473,474,479,482],{},[125,475,476],{},[21,477,478],{},"PLS",[125,480,481],{},"Partial Least Squares (on PCA)",[125,483,484],{},"12.79",[58,486,488],{"id":487},"linear-mixed-effects-models-lmm","Linear Mixed-Effects Models (LMM)",[18,490,491],{},"Advanced panel data models accounting for asset-specific effects:",[101,493,494,506],{},[104,495,496],{},[107,497,498,500,503],{},[110,499,412],{},[110,501,502],{},"Features",[110,504,505],{},"RMSE",[120,507,508,519,530,540,551],{},[107,509,510,513,516],{},[125,511,512],{},"LMM Baseline",[125,514,515],{},"All variables + Random Intercept",[125,517,518],{},"8.77",[107,520,521,524,527],{},[125,522,523],{},"LMM Reduced",[125,525,526],{},"Collinearity removal",[125,528,529],{},"~8.77",[107,531,532,535,538],{},[125,533,534],{},"LMM Interactions",[125,536,537],{},"Financial interaction terms",[125,539,529],{},[107,541,542,545,548],{},[125,543,544],{},"LMM + Quadratic",[125,546,547],{},"Convexity terms (vol of vol)",[125,549,550],{},"8.41",[107,552,553,558,561],{},[125,554,555],{},[21,556,557],{},"LMM + Random Slopes (mod_lmm_5)",[125,559,560],{},"Asset-specific betas",[125,562,563,566],{},[21,564,565],{},"8.10"," ⭐",[58,568,570],{"id":569},"tree-based-models","Tree-Based Models",[101,572,573,588],{},[104,574,575],{},[107,576,577,579,582,585],{},[110,578,412],{},[110,580,581],{},"Strategy",[110,583,584],{},"Validation RMSE",[110,586,587],{},"Training RMSE",[120,589,590,606,624],{},[107,591,592,597,600,603],{},[125,593,594],{},[21,595,596],{},"XGBoost",[125,598,599],{},"Level-wise, Bayesian tuning",[125,601,602],{},"10.70",[125,604,605],{},"0.57",[107,607,608,613,616,621],{},[125,609,610],{},[21,611,612],{},"LightGBM",[125,614,615],{},"Leaf-wise, feature regularization",[125,617,618,566],{},[21,619,620],{},"10.61",[125,622,623],{},"10.90",[107,625,626,629,632,635],{},[125,627,628],{},"Random Forest",[125,630,631],{},"Bagging",[125,633,634],{},"DNF*",[125,636,637],{},"-",[18,639,640],{},"*DNF: Did Not Finish (computational constraints)",[58,642,644],{"id":643},"neural-networks","Neural Networks",[101,646,647,659],{},[104,648,649],{},[107,650,651,653,656],{},[110,652,412],{},[110,654,655],{},"Architecture",[110,657,658],{},"Status",[120,660,661],{},[107,662,663,666,669],{},[125,664,665],{},"MLP",[125,667,668],{},"128-64 units, tanh activation",[125,670,671],{},"Failed to converge",[50,673],{},[53,675,677],{"id":676},"results-summary","Results Summary",[58,679,681],{"id":680},"model-comparison","Model Comparison",[258,683,686],{"className":684,"code":685,"language":263},[261],"RMSE Performance (Lower is Better)\n━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\nLinear Mixed-Effects (LMM5)     8.38 ████████████████████ Best Linear\nLinear Mixed-Effects (LMM4)     8.41 ███████████████████\nLinear Mixed-Effects (Baseline) 8.77 ██████████████████\n━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\nLightGBM                       10.61 ███████████████ Best Non-Linear\nXGBoost                        10.70 ██████████████\n━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\nOLS (with interactions)        11.26 █████████████\nLasso                          12.03 ███████████\nOLS (baseline)                 12.01 ███████████\nRidge                          12.48 ██████████\nPLS                            12.79 █████████\n━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\n",[128,687,685],{"__ignoreMap":266},[58,689,691],{"id":690},"key-findings","Key Findings",[693,694,695,709,723],"ol",{},[36,696,697,700,701],{},[21,698,699],{},"Best Linear Model:"," LMM with Random Slopes (RMSE = 8.38)",[33,702,703,706],{},[36,704,705],{},"Captures asset-specific volatility sensitivities",[36,707,708],{},"Includes quadratic terms for convexity effects",[36,710,711,714,715],{},[21,712,713],{},"Best Non-Linear Model:"," LightGBM (RMSE = 10.61)",[33,716,717,720],{},[36,718,719],{},"Superior generalization vs XGBoost",[36,721,722],{},"Feature regularization prevents overfitting",[36,724,725,728],{},[21,726,727],{},"Interpretability Insights (SHAP Analysis):",[33,729,730,736,739],{},[36,731,732,735],{},[128,733,734],{},"realized_vol_mid"," dominates (57% of gain)",[36,737,738],{},"Volatility clustering confirmed as primary driver",[36,740,741],{},"Non-linear regime switching in stress_spread",[50,743],{},[53,745,747],{"id":746},"repository-structure","Repository Structure",[258,749,752],{"className":750,"code":751,"language":263},[261],"PROJECT\u002F\n├── Projet_MRC_DANJOU_LEGRAND_MERIC_VONSIEMENS.qmd     # Main analysis (Quarto)\n├── Projet_MRC_DANJOU_LEGRAND_MERIC_VONSIEMENS.html    # Rendered report\n├── packages.R                                         # R dependencies installer\n├── Train_ISF.csv                                      # Training data (~1.9M rows)\n├── Test_ISF.csv                                       # Test data (~1.25M rows)\n├── hat_y.csv                                          # Final predictions\n├── README.md                                          # This file\n└── results\u002F\n    ├── lightgbm\u002F                                      # LightGBM model outputs\n    └── xgboost\u002F                                       # XGBoost model outputs\n",[128,753,751],{"__ignoreMap":266},[50,755],{},[53,757,759],{"id":758},"getting-started","Getting Started",[58,761,763],{"id":762},"prerequisites","Prerequisites",[33,765,766,772],{},[36,767,768,771],{},[21,769,770],{},"R"," ≥ 4.0",[36,773,774,775,778],{},"Required packages (auto-installed via ",[128,776,777],{},"packages.R",")",[58,780,782],{"id":781},"installation","Installation",[258,784,788],{"className":785,"code":786,"language":787,"meta":266,"style":266},"language-r shiki shiki-themes material-theme-lighter catppuccin-latte catppuccin-macchiato","# Install all dependencies\nsource(\"packages.R\")\n","r",[128,789,790,798],{"__ignoreMap":266},[791,792,795],"span",{"class":793,"line":794},"line",1,[791,796,797],{},"# Install all dependencies\n",[791,799,801],{"class":793,"line":800},2,[791,802,803],{},"source(\"packages.R\")\n",[18,805,806],{},"Or manually install key packages:",[258,808,810],{"className":785,"code":809,"language":787,"meta":266,"style":266},"install.packages(c(\n  \"tidyverse\", \"tidymodels\", \"caret\", \"glmnet\",\n  \"lme4\", \"lmerTest\", \"xgboost\", \"lightgbm\",\n  \"ranger\", \"pls\", \"shapviz\", \"rBayesianOptimization\"\n))\n",[128,811,812,817,822,828,834],{"__ignoreMap":266},[791,813,814],{"class":793,"line":794},[791,815,816],{},"install.packages(c(\n",[791,818,819],{"class":793,"line":800},[791,820,821],{},"  \"tidyverse\", \"tidymodels\", \"caret\", \"glmnet\",\n",[791,823,825],{"class":793,"line":824},3,[791,826,827],{},"  \"lme4\", \"lmerTest\", \"xgboost\", \"lightgbm\",\n",[791,829,831],{"class":793,"line":830},4,[791,832,833],{},"  \"ranger\", \"pls\", \"shapviz\", \"rBayesianOptimization\"\n",[791,835,837],{"class":793,"line":836},5,[791,838,839],{},"))\n",[58,841,843],{"id":842},"running-the-analysis","Running the Analysis",[693,845,846,866,880],{},[36,847,848,851],{},[21,849,850],{},"Open the Quarto document:",[258,852,854],{"className":785,"code":853,"language":787,"meta":266,"style":266},"# In RStudio\nrstudioapi::navigateToFile(\"Projet_MRC_DANJOU_LEGRAND_MERIC_VONSIEMENS.qmd\")\n",[128,855,856,861],{"__ignoreMap":266},[791,857,858],{"class":793,"line":794},[791,859,860],{},"# In RStudio\n",[791,862,863],{"class":793,"line":800},[791,864,865],{},"rstudioapi::navigateToFile(\"Projet_MRC_DANJOU_LEGRAND_MERIC_VONSIEMENS.qmd\")\n",[36,867,868,871],{},[21,869,870],{},"Render the document:",[258,872,874],{"className":785,"code":873,"language":787,"meta":266,"style":266},"quarto::quarto_render(\"Projet_MRC_DANJOU_LEGRAND_MERIC_VONSIEMENS.qmd\")\n",[128,875,876],{"__ignoreMap":266},[791,877,878],{"class":793,"line":794},[791,879,873],{},[36,881,882,885,886,889],{},[21,883,884],{},"Or run specific sections interactively"," using the code chunks in the ",[128,887,888],{},".qmd"," file",[50,891],{},[53,893,895],{"id":894},"technical-details","Technical Details",[58,897,899],{"id":898},"data-split-strategy","Data Split Strategy",[33,901,902,908,911,914],{},[36,903,904,907],{},[21,905,906],{},"Chronological split"," at 80th percentile of dates",[36,909,910],{},"Prevents look-ahead bias and data leakage",[36,912,913],{},"Training: ~1.53M observations",[36,915,916],{},"Validation: ~376K observations",[58,918,920],{"id":919},"hyperparameter-tuning","Hyperparameter Tuning",[33,922,923,929,935],{},[36,924,925,928],{},[21,926,927],{},"Method:"," Bayesian Optimization (Gaussian Processes)",[36,930,931,934],{},[21,932,933],{},"Acquisition:"," Expected Improvement (UCB)",[36,936,937,940],{},[21,938,939],{},"Goal:"," Maximize negative RMSE",[58,942,944],{"id":943},"evaluation-metric","Evaluation Metric",[18,946,947,950],{},[21,948,949],{},"Exponential RMSE"," on original 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