Arbitrage-Free Prediction of the Implied Volatility Surface with Temporal Attention

Overview

This repository contains the code and resources for the honors thesis titled "Arbitrage-Free Prediction of the Implied Volatility Surface with Temporal Attention Strategy." The project focuses on developing a model to predict the future Implied Volatility Surface (IVS) for options on the SPDR S&P 500 ETF (SPY), ensuring that these predictions are free from static arbitrage.

The core methodology involves:

1. Feature Extraction: Comparing two approaches:
   • A Variational Autoencoder (VAE) to create a lower-dimensional latent representation of the IVS.
   • Direct sampling of IVS points.
2. Exogenous Data Integration: Incorporating 10 exogenous market features (e.g., VIX levels, SPY volume, day of the week/month) to provide broader market context.
3. Prediction Model: Utilizing a Long Short-Term Memory (LSTM) neural network enhanced with a multi-head temporal attention mechanism.
4. Arbitrage-Free Enforcement: Employing a Deep Neural Network (DNN) to adjust the predicted IVS, ensuring it adheres to no-static-arbitrage conditions.

The study found that the IVS sampling approach, when combined with the multi-head temporal attention mechanism, yielded superior predictive capability.

Key Visualizations

Here are some visualizations from the research:

• Example Implied Volatility Surface:
• Model Performance Comparison (RMSE):
• LSTM Training Loss (Sampling Method):

(More visualizations can be found in the visualizations/ directory.)

Repository Structure & Notebooks

The project is organized into a series of Jupyter notebooks, executed in sequence:

• S1_IVS_construction.ipynb: Constructs the Implied Volatility Surface from raw options data.
• S2_surface_sampling.ipynb: Implements methods for sampling points from the IVS.
• S3_STD_IVS_viz.ipynb: Visualizes the constructed standard IVS.
• S4_IVS_ARB_Break_viz.ipynb: Visualizes instances of arbitrage breaks in the IVS.
• S5_train_VAE.ipynb: Trains the Variational Autoencoder for feature extraction.
• S6_grab_exogenous_variables.ipynb: Gathers and preprocesses exogenous market variables.
• S7_train_LSTM.ipynb: Trains the LSTM with multi-head temporal attention for IVS prediction.
• S8_statarb_free_DNN.ipynb: Trains the Deep Neural Network to ensure static arbitrage-free predictions.
• S9_testing.ipynb: Conducts out-of-sample testing and evaluates the performance of the complete model pipeline using metrics like RMSE, MAPE, and MDA.

Research Paper

The full honors thesis detailing the methodology, results, and discussion can be accessed here:

• Arbitrage-Free Prediction of the Implied Volatility Surface with Temporal Attention

Technologies Used

• Python 3
• Jupyter Notebooks
• PyTorch (torch, torch.nn, torch.utils.data, torch.optim, torch.autograd)
• torchvision (for transforms)
• Pandas
• NumPy
• scikit-learn (StandardScaler, MinMaxScaler)
• Matplotlib / Seaborn
• IPython (for display utilities)
• pickle (for data serialization)

Future Work

Potential areas for future research include:

• Exploring advanced attention mechanisms, such as pruning attention heads or transformer-based systems.
• Investigating additional exogenous variables for improved market sentiment capture.

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