How Is Implied Volatility Calculated from the Black-Scholes Model?
Implied volatility is not calculated directly from the Black-Scholes formula; rather, it is found by reversing the process. The model's formula is used to solve for the volatility that would make the theoretical option price equal to the current market price of that option.
Since there is no simple algebraic solution for volatility in the formula, this requires an iterative numerical method, such as the Newton-Raphson method. Traders input the known variables (stock price, strike price, time to expiration, risk-free rate) and the option's market price, and the algorithm finds the volatility value that fits.
Glossar
Implied Volatility
Expectation ⎊ This value represents the market's consensus forecast of future asset price fluctuation, derived by reversing option pricing models using current market premiums.
Theoretical Option Price
Valuation ⎊ A theoretical option price, within cryptocurrency markets, represents a calculated estimate of an option’s fair value, derived from a mathematical model incorporating factors like the underlying asset’s price, strike price, time to expiration, volatility, and risk-free interest rate.
Black-Scholes Formula
Derivation ⎊ The Black-Scholes Formula, initially proposed in 1973, provides a theoretical estimate of the price of European-style options, fundamentally altering quantitative finance and risk management practices.