The implied standard Deviation or implied volatility is the volatility value that would make the theoretical value (in this case the Black-Scholes Model) equals to the given market price. To use Newton-Ralphson method, the first differential of the standard deviation with respect to the price (Black/Scholes) is required. In this case, we can use Vega (Kappa) the sensitivity of the call price to the implied standard deviation.
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