A Theoretical Analysis of Implied Volatility and Its Determinants under the Black-Scholes Framework

Abstract

: Options have become indispensable instruments for both risk management and speculation, with volatility serving as a fundamental input in pricing structures. While Historical Volatility (HV) relies on past returns, it is inherently backward-looking and fails to reflect forward-looking market expectations, investor sentiment, or risk aversion. Conversely, Implied Volatility (IV), derived through the inverse mapping of the Black – Scholes (BS) model, effectively synthesizes future uncertainty, collective expectations, and risk premia. This paper provides a thorough theoretical analysis of IV within the BS framework, examining its definition, determinants, and dual-component nature — comprising expected realized volatility and the volatility risk premium. The study further interprets the volatility term structure and the "smile" or "skew" phenomena as market compensations for the BS model's limiting assumptions of constant volatility and normal distribution. By elucidating why IV typically commands a premium over realized volatility, this research offers a critical theoretical foundation for subsequent quantitative studies, option hedging strategies, and risk management practices.