Iterative Calibration of Implied Volatility for European Options: A Computational Approach

Implied volatility is a crucial variable for options trading as it helps determine profitability. It reflects the future movement of the underlying asset’s price and predicts the extent of potential price fluctuation, which can be used to determine if options are likely to be profitable before expiry. The main focus of this research paper is on an iterative numerical method used to calculate the implied volatility of European options. This value is a crucial component in determining the option price. The Black–Scholes model, which assumes that the underlying asset’s volatility is constant and known, does not reflect the reality of the market. Empirical and theoretical studies have shown that the implied volatility of the underlying asset prices follows a persistent smile pattern, indicating a clear relationship between the option strike price and its implied volatility. Moreover, the volatility term structure reflects the relationship between the implied volatility and the time to option expiration, which is not constant. The research aims to provide a better understanding of the complex dynamics of implied volatility and its impact on options trading profitability.