Extracting implied information, like volatility and dividend, from observed option prices is a challenging task when dealing with American options, because of the complex-shaped early-exercise regions and the computational costs to solve the corresponding mathematical problem repeatedly. We will employ a data-driven machine learning approach to estimate the Black-Scholes implied volatility and the dividend yield for American options in a fast and robust way. To determine the implied volatility, the inverse function is approximated by an artificial neural network on the effective computational domain of interest, which decouples the offline (training) and online (prediction) stages and thus eliminates the need for an iterative process. In the case of an unknown dividend yield, we formulate the inverse problem as a calibration problem and determine simultaneously the implied volatility and dividend yield. For this, a generic and robust calibration framework, the Calibration Neural Network (CaNN), is introduced to estimate multiple parameters. It is shown that machine learning can be used as an efficient numerical technique to extract implied information from American options, particularly when considering multiple early-exercise regions due to negative interest rates.

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Applied Mathematical Finance
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Liu, S, Leitao Rodriguez, Á, Borovykh, A.I, & Oosterlee, C.W. (2022). On a neural network to extract implied information from American options. Applied Mathematical Finance, 28(5), 449–475. doi:10.1080/1350486X.2022.2097099