Neural Networks for Options Pricing

An option’s value depends on factors such as the underlying price, strike, time to expiry, volatility, interest rates, and contract terms. Traditional models such as Black–Scholes provide a mathematical baseline under specified assumptions. Neural networks can approximate a pricing function from simulated or observed examples, and researchers have studied using networks to estimate prices and hedging sensitivities. An approximation may be fast after training, but it can be inaccurate outside the data distribution or when assumptions do not fit market conditions. Training on model-generated prices only learns to approximate that source model; it does not show that the source model reflects market prices. Training on observed quotes introduces issues such as stale data, bid-ask spreads, liquidity, and noisy labels. Sensitivities such as delta are derivatives of the learned pricing function and may be unstable where data are sparse. Evaluate prices and hedges out of sample, across strikes, maturities, volatility regimes, and asset types. Compare with established models and market quotes, quantify error and uncertainty, and define a fallback for out-of-range inputs. Do not treat a model price as an instruction to trade. Model risk, transaction costs, liquidity, and portfolio constraints remain important to a pricing or hedging decision. Market data are not frictionless: quotes may be stale, spreads vary, and some contracts trade rarely. A model should signal when inputs are missing or outside its supported domain rather than silently returning a confident price.