I observe that Christoffersen et al. (2012) consider the implied volatility from European options, as calculated under the BS model and other extensions of it. Therefore, implied volatilities from American options cannot be used for the methods described in this paper, as they are slightly different and reflect incremental information over the "early-exercise premium".
To overcome this issue, American option prices should be De-Americanized. A summary of the De-Americanization scheme is provided by Maglione (2020):
The aim of the de-Americanization is to find the corresponding
European price (the so-called pseudo-European price) for a given
American price. That is, the price ought to be observed if the
contract would not allow to exercise the option before maturity. In a
nutshell, a binomial tree is used to price the American option. The
volatility parameter such that the squared difference between the
market price and the price generated by the tree is minimised is set
as the option implied volatility. Once estimated, the pseudo-European
price is found by applying the Black-Scholes formula for European
For more details, please refer to the sources listed below.
Christoffersen, Peter, Kris Jacobs, and Bo Young Chang. "Forecasting with option-implied information." Handbook of economic forecasting 2 (2013): 581-656.
Carr, Peter, and Liuren Wu. "Stock options and credit default swaps: A joint framework for valuation and estimation." Journal of Financial Econometrics 8, no. 4 (2010): 409-449.
Burkovska, Olena, Maximilian Gass, Kathrin Glau, Mirco Mahlstedt, Wim Schoutens, and Barbara Wohlmuth. "Calibration to American options: numerical investigation of the de-Americanization method." Quantitative finance 18, no. 7 (2018): 1091-1113.
Maglione, Federico. "The use of compound options for credit risk modelling." PhD diss., City, University of London, 2020.