From Black-Scholes to Jump-Diffusion: A Narrative Review of Option pricing Model Evolution

Abstract

Option pricing theory is a cornerstone of modern financial engineering, but the classical Black-Scholes framework relies on continuous price trajectories, constant volatility, and lognormally distributed returns. These assumptions are difficult to reconcile with empirical features such as volatility smiles, fat-tailed returns, volatility clustering, and abrupt price movements. This review examines the evolution of Option pricing models from the Black-Scholes benchmark to stochastic-volatility, jump-diffusion, stochastic-volatility-jump, and affine jump-diffusion specifications. It shows that richer models generally improve cross-sectional pricing accuracy, especially for short-maturity and out-of-the-money options, but that this improvement is accompanied by higher parameter uncertainty, calibration complexity, and hedging instability. The review further emphasizes that evidence from emerging markets, particularly China’s domestic derivatives market, remains comparatively limited and may require models that account for liquidity constraints, retail participation, and clustered jump behavior.