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I have recently been researching European options versus American options implied information. For European options, an overview article is Christoffersen(2012). But for American options, I only found some articles on extracting implied volatility. Christoffersen(2012) said, "The early exercise premium must be estimated and subtracted from the American option price before using the method surveyed in this chapter." I would like to know if there is any literature that explains this idea in detail.

Any overview article relating to the information content of the American options and European options markets is welcome.

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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 options.

For more details, please refer to the sources listed below.

Sources:

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.

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