Option valuation under no-arbitrage constraints with neural networks

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