Implied Volatility Surface Modeling

This project targets high-precision calibration of the Implied Volatility Surface using a large-scale dataset of S&P 500 (SPX) European options.

The core objective is to stress-test classic statistical models against modern predictive algorithms. Generalized Linear Models (GLMs) provide a transparent baseline, while more complex "black-box" architectures are evaluated on whether their accuracy gains justify reduced interpretability in a risk management context.

📊 Dataset & Scale

The modeling is performed on a high-dimensional dataset with over 1.2 million observations.

• Target Variable: implied_vol_ref (implied volatility).
• Features: Option strike price ($K$), underlying asset price ($S$), and time to maturity ($\tau$).
• Volume: A training set of $1,251,307$ rows and a test set of identical size.

🛠️ Modeling Methodology

The project follows a rigorous statistical pipeline to compare two modeling philosophies:

1. The Statistical Baseline (GLM)

Using R's GLM framework, I implement models with targeted link functions and error distributions (such as Gamma or Inverse Gaussian) to capture the global structure of the volatility surface. These models serve as the benchmark for transparency and stability.

2. The Black-Box Challenge

To capture local non-linearities such as the volatility smile and skew, I explore more complex architectures. Performance is evaluated by Root Mean Squared Error (RMSE) relative to the GLM baselines.

3. Feature Engineering

Key financial indicators are derived from the raw data:

• Moneyness: Calculated as the ratio $K/S$.
• Temporal Dynamics: Transformations of time to maturity to linearize the term structure.

📈 Evaluation & Reproducibility

Performance is measured strictly via RMSE on the original scale of the target variable. To ensure reproducibility and precise comparisons across model iterations, a fixed random seed is maintained throughout the workflow.

set.seed(2025)

TrainData <- read.csv("train_ISF.csv", stringsAsFactors = FALSE)
TestX <- read.csv("test_ISF.csv", stringsAsFactors = FALSE)

rmse_eval <- function(actual, predicted) {
  sqrt(mean((actual - predicted)^2))
}

🔍 Critical Analysis

Beyond pure prediction, the project addresses:

• Model Limits: Identifying market regimes where models fail (e.g., deep out-of-the-money options).
• Interpretability: Quantifying the trade-off between complexity and practical utility in a risk management context.
• Future Extensions: Considering richer dynamics, such as historical volatility or skew-specific targets.