Option valuation under no-arbitrage constraints with neural networks

Yi Cao, Xiaoquan Liu*, Jia Zhai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


In this paper, we start from the no-arbitrage constraints in option pricing and develop a novel hybrid gated neural network (hGNN) based option valuation model. We adopt a multiplicative structure of hidden layers to ensure model differentiability. We also select the slope and weights of input layers to satisfy the no-arbitrage constraints. Meanwhile, a separate neural network is constructed for predicting option-implied volatilities. Using S&P 500 options, our empirical analyses show that the hGNN model substantially outperforms well-established alternative models in the out-of-sample forecasting and hedging exercises. The superior prediction performance stems from our model's ability in describing options on the boundary, and in offering analytical expressions for option Greeks which generate better hedging results.

Original languageEnglish
Pages (from-to)361-374
Number of pages14
JournalEuropean Journal of Operational Research
Issue number1
Publication statusPublished - 16 Aug 2021


  • Artificial neural networks
  • Finance
  • Hedging
  • Implied volatilities
  • Option greeks


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