Option Pricing in Motion: Volatility, States, and Risk

Abstract

: This paper develops a comprehensive theoretical framework for option pricing in dynamic markets characterized by volatility fluctuations, regime changes, and risk sensitivities (Greeks). While the Black – Scholes model assumes constant volatility, real markets exhibit volatility smiles, skews, jumps, and distinct regimes. Existing literature has studied local volatility, stochastic volatility, regime switching, and Greeks largely in isolation. This paper integrates these dimensions by conceptualizing option pricing as a propagation mechanism. Specifically, market regimes influence key characteristics of the underlying process, including drift, volatility, correlations, and jump intensities. These regime-dependent features shape the volatility process and generate implied volatility surfaces across strikes and maturities. The implied volatility surface, in turn, embeds regime information into option prices, while Greeks translate price adjustments into measurable risk sensitivities. By linking regimes, volatility structures, option prices, and Greeks within a unified framework, the paper clarifies how state transitions propagate through volatility models into pricing and risk management. The analysis highlights the interdependence of these elements and suggests that such integration can improve model interpretation, implied volatility analysis, and regime-aware risk management. Future research may focus on empirical validation, liquidity frictions, and regime detection using data-driven methods.