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In the paper written by Klibanov et al, it proposes a novel method tocalculate implied volatility of a European stock options as a solution toill-posed inverse problem for the Black-Scholes equation. In addition, itproposes a trading strategy based on the difference between implied volatilityof the option and the volatility of the underlying stock. In addition to theBlack-Scholes equation, Binomial model is another method used to price Europeanoptions. And, the implied volatility can be also calculated through this model.In this paper, we apply the Newton-Raphson method together with AutomaticDifferention to numerically approximate the implied volatility of an arbitrarystock option through this model. We provide an explanation of the mathematicalmodel and methods, the methodology, and the results from our test using thestimulated data from the Geometric Brownian Motion Model and the Binomial Modelitself, and the data from the US market data from 2018 to 2021.

Using the Newton-Raphson Method with Automatic Differentiation to Numerically Solve Implied Volatility of Stock Option through Binomial Model