Deep Learning Option Pricing with Market Implied Volatility Surfaces

Paper: arXiv 2509.05911

Authors: Lijie Ding, Egang Lu, Kin Cheung

Abstract

We present a deep learning framework for pricing options based on market-implied volatility surfaces. Using end-of-day S&P 500 index options quotes from 2018-2023, we construct arbitrage-free volatility surfaces and generate training data for American puts and arithmetic Asian options using QuantLib. To address the high dimensionality of volatility surfaces, we employ a variational autoencoder (VAE) that compresses volatility surfaces across maturities and strikes into a 10-dimensional latent representation. We feed these latent variables, combined with option-specific inputs such as strike and maturity, into a multilayer perceptron to predict option prices. Our model is trained in stages: first to train the VAE for volatility surface compression and reconstruction, then options pricing mapping, and finally fine-tune the entire network end-to-end. The trained pricer achieves high accuracy across American and Asian options, with prediction errors concentrated primarily near long maturities and at-the-money strikes, where absolute bid-ask price differences are known to be large. Our method offers an efficient and scalable approach requiring only a single neural network forward pass and naturally improve with additional data. By bridging volatility surface modeling and option pricing in a unified framework, it provides a fast and flexible alternative to traditional numerical approaches for exotic options.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced neural network architectures (VAE, MLP) with detailed mathematical formulation for compression and mapping, indicating high mathematical complexity. It demonstrates strong empirical rigor by using real market data from 2018-2023, constructing arbitrage-free surfaces, generating training/testing splits, and providing error analysis and performance metrics.

Research Flowchart

  flowchart TD
  A["Research Goal: Develop fast, scalable option pricer<br>using market-implied volatility surfaces"] --> B
  subgraph B ["Data & Preprocessing"]
      B1["S&P 500 Index Options<br>2018-2023"] --> B2["Construct Arbitrage-Free<br>Volatility Surfaces"]
  end
  B --> C
  subgraph C ["Deep Learning Architecture"]
      C1["VAE Encoder<br>Compresses Surface to 10-D Latent"] --> C2["Multilayer Perceptron<br>Maps Latent + Inputs to Price"]
  end
  C --> D["Staged Training:<br>1. VAE Training 2. MLP Mapping 3. End-to-End Fine-Tune"]
  D --> E
  subgraph E ["Key Outcomes"]
      E1["High Accuracy<br>American & Asian Options"]
      E2["Errors Near Long Maturity<br>& At-the-Money Strikes"]
      E3["Efficient Forward Pass<br>Superior Scalability"]
  end

Cited References (39)

1. The Pricing of Options and Corporate Liabilities (1973)
2. Paul Wilmott on quantitative finance (2013)
3. Stochastic calculus for finance II: Continuous-time models (2004)
4. Options, Futures, and Other Derivatives (2017)
5. Financial modelling with jump processes (2003)
6. Monte Carlo Methods in Financial Engineering (2004)
7. Dynamic asset pricing theory (2010)
8. Machine learning: a probabilistic perspective (2012)

1 of 39 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.