A Study of Option Pricing Models with Market Price Adjustments: Empirical Analysis Beyond the Black-Scholes Model

In 1973, Fischer Black and Myron Scholes unveiled the Black-Scholes option pricing model, a groundbreaking contribution that profoundly influenced the domain of option pricing theory. The introduction of the Black-Scholes pricing formula has garnered substantial acclaim across both academic and industrial spheres, leading to its widespread dissemination and application. This formula not only underscores its vital significance but also exemplifies its unique position as a cornerstone of financial theory, reshaping how options are valued and traded in markets worldwide.

However, in the real financial market, the Black-Scholes option pricing model has a serious deviation from empirical research in option pricing, which reduces its practicality and accuracy. This paper first briefly introduces the basic knowledge of options, covering both option-related concepts and option pricing theories, gives the definition of Black-Scholes option pricing deviation, and explains the volatility smile theory in detail. Starting from the probability of positive returns and the beliefs of traders, the probability of call option returns is obtained from historical trading data, and then decisions are made from these probabilities to overcome the deviations caused by Black-Scholes European option pricing and find an option pricing model that is more consistent with the market price of options.

Through comprehensive simulation studies utilizing synthesized data, we conduct rigorous empirical tests to compare this theoretical model with the Black-Scholes option pricing model. The market prices of call options are derived from investor sentiments, allowing us to validate all three types of deviations from the Black-Scholes pricing formula within this numerical framework. The results reveal that the growth rates of stock returns can effectively serve as a substitute for the volatility smile, thereby facilitating their exclusion from risk-neutral analyses.

These insights significantly enhance our understanding of option pricing dynamics in real-world scenarios.