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A Two-Step Framework for Arbitrage-Free Prediction of the Implied Volatility Surface

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Listed:
  • Wenyong Zhang
  • Lingfei Li
  • Gongqiu Zhang
Abstract
We propose a two-step framework for predicting the implied volatility surface over time without static arbitrage. In the first step, we select features to represent the surface and predict them over time. In the second step, we use the predicted features to construct the implied volatility surface using a deep neural network (DNN) model by incorporating constraints that prevent static arbitrage. We consider three methods to extract features from the implied volatility data: principal component analysis, variational autoencoder and sampling the surface, and we predict these features using LSTM. Using a long time series of implied volatility data for S\&P500 index options to train our models, we find two feature construction methods, sampling the surface and variational autoencoders combined with DNN for surface construction, are the best performers in out-of-sample prediction. In particular, they outperform a classical method substantially. Furthermore, the DNN model for surface construction not only removes static arbitrage, but also significantly reduces the prediction error compared with a standard interpolation method. Our framework can also be used to simulate the dynamics of the implied volatility surface without static arbitrage.

Suggested Citation

  • Wenyong Zhang & Lingfei Li & Gongqiu Zhang, 2021. "A Two-Step Framework for Arbitrage-Free Prediction of the Implied Volatility Surface," Papers 2106.07177, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2106.07177
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    References listed on IDEAS

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