Can a dealer's behavior predict stock fluctuations? This research investigates the applicability of the Langevin equation model to the Italian stock market, specifically "Assicurazioni Generali," offering insights into more general pricing and hedging models. Unlike the Black-Scholes model, which often fails to capture true market dynamics, this study explores alternative approaches to understanding and managing financial risk. By examining the stock's behavior through the lens of the Langevin equation, the authors aim to determine the density function of both multiplicative and additive noise, revealing the Lévy distribution for changes. This distribution aligns with the observed histograms and Kernel estimates, offering a more accurate representation of market fluctuations. This distribution is consistent with the histograms and the Kernel estimates. The results are then applied to develop hedging strategies, drawing on the work of Sornette and Bouchaud. This research has implications for understanding financial markets and improving hedging models, particularly in scenarios where traditional assumptions are not met. Further studies may explore the model's effectiveness across different markets and its adaptability to changing market conditions.
Published in the International Journal of Theoretical and Applied Finance, this paper aligns with the journal's focus on quantitative finance and innovative financial modeling. By applying the Langevin equation to stock hedging, the study contributes to the journal's interest in alternative financial strategies that improve hedging models within the stock market.