A Neural Network approach to assess volatility implied by market data

Volatility has gained a central role in financial markets due to its widespread application across multiple domains. Practitioners and academics regard it as a crucial measure of risk, significant for derivatives pricing models, and relevant for monetary policy decision-making. Traditional methods for estimating volatility fall into two main categories: time-series models, which leverage historical data, and methods that infer volatility from option prices. Despite the extensive material in the literature, these approaches often face criticism regarding their strong assumptions and limited flexibility. To address these limitations, model-free alternatives like artificial neural networks can represent an effective solution thanks to their universal approximator property. In this study, multi-layer perceptrons are trained on real-world financial data to approximate volatility implied in OTM S&P 500 one-month options, based on Black-Scholes-Merton (BSM) input features and Volatility Index values. An analysis of error measures evaluates the performance of the trained multi-layer perceptrons, followed by an example that compares the networks with BSM formula on unseen data across multiple strike prices.