Machine Learning to Compute Implied Volatility from European/American Options Considering Dividend Yield

Abstract

Computing implied volatility from observed option prices is a frequent and challenging task in finance, even more in the presence of dividends. In this work, we employ a data-driven machine learning approach to determine the Black–Scholes implied volatility, including European-style and American-style options. The inverse function of the pricing model is approximated by an artificial neural network, which decouples the offline (training) and online (prediction) phases and eliminates the need for an iterative process to solve a minimization problem. Meanwhile, two challenging issues are tackled to improve accuracy and robustness, i.e., steep gradients of the volatility with respect to the option price and irregular early-exercise domains for American options. It is shown that deep neural networks can be used as an efficient numerical technique to compute implied volatility from European/American options. An extended version of this work can be found in .