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This essay explores the evolution of option pricing models, tracing their development from the foundational Black-Scholes model to more advanced frameworks such as the Heston model and beyond. Beginning with an introduction to option pricing theory, the essay discusses the origins of the Black-Scholes model and its assumptions, as well as the challenges and limitations it faces. It then examines the extension of the Black-Scholes model, so-called the Black-Scholes-Merton model. It incorporates dividends, and lays the groundwork for further research into options pricing and financial derivatives. Then various stochastic volatility models emerge, and the essay chooses the Heston model as a typical example for analysis, highlighting its advantages and applications in option pricing. Furthermore, the essay compares the Heston model with other option pricing models, including the SABR model and Bates model. At the end of the essay, recent advances and future directions in option pricing are introduced and discussed. Through this comprehensive exploration, readers can gain a deeper understanding of the evolution of option pricing models and their significance in modern finance.
Xilin Hong (Mon,) studied this question.