Operator Deep Smoothing for Implied Volatility

Authors: Ruben Wiedemann, Antoine (Jack) Jacquier, Lukas Gonon

ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We provide extensive historical benchmarks and showcase the generalization capability of our approach in a comparison with classical neural networks and SVI, an industry standard parametrization for implied volatility. We perform our numerical experiments using 20-minute interval CBOE S&P 500 Index Option data from 2012 to 2021. The dataset amounts to a collection of 49089 implied volatility surfaces and just above 60 million individual volatility datapoints (after domain truncation).
Researcher Affiliation Academia Ruben Wiedemann Imperial College London EMAIL Antoine Jacquier Imperial College London EMAIL Lukas Gonon University of St. Gallen EMAIL
Pseudocode No The paper describes the modifications to the GNO architecture and the forward propagation steps in text and mathematical formulas (Appendix B) but does not provide a clearly labeled pseudocode or algorithm block.
Open Source Code Yes Code We make code for the paper available at the location https://github.com/rwicl/operator-deep-smoothing-for-implied-volatility. In particular, the code repository contains a general Py Torch (Paszke et al., 2019) implementation of the graph neural operator architecture for operator deep smoothing.
Open Datasets Yes To do so, one would need to download the data from WRDS, persist it at prespecified location detailed in the codebase, and then run the respective notebooks, which automatically load the trained model weights. The Option Metrics end-of-day options data for the suite of indices considered in the final paragraph of Section 4, on the other hand, is more readily and freely available to researchers with subscriptions via the Wharton Research Data Services (WRDS) platform.
Dataset Splits Yes We perform our numerical experiments using 20-minute interval CBOE S&P 500 Index Option data from 2012 to 2021. The dataset amounts to a collection of 49089 implied volatility surfaces and just above 60 million individual volatility datapoints (after domain truncation). We refer the reader to Appendix C.1 for details on the preparation of the dataset. We allocate the first nine years of data (2012 to 2020) to training, keeping 750 randomly drawn surfaces for validation purposes, and use the final year of the dataset (2021) for testing. This yields a training dataset Dtrain containing ntrain = 43442 surfaces, a validation dataset Dval containing nval = 750 surfaces, and a test dataset Dtest with ntest = 4897 surfaces.
Hardware Specification Yes The training is performed in around 250 hours using an NVIDIA Quadro RTX 6000 GPU. We benchmarked the execution with nin = 897 and nout = 2500 (i.e., with an output grid of size 50 50) on a consumer-grade laptop CPU as well as an Nvidia Quadro RTX 6000 GPU in Table 10.
Software Dependencies Yes In particular, the code repository contains a general Py Torch (Paszke et al., 2019) implementation of the graph neural operator architecture for operator deep smoothing.
Experiment Setup Yes The model hyperparameters (giving rise to 102529 trainable parameters in total) were identified by manual experimentation and are detailed in Appendix C.2. We train the GNO for 500 epochs on Dtrain using the Adam W optimizer with learning rate λ = 10 4 and weight decay rate β = 10 5, and use a pseudo batch size of 64 by accumulating gradients.