Wednesday 09 April 2025
The quest for a more accurate model of stock market behavior has led researchers to venture into uncharted territories, combining concepts from physics and mathematics to better understand the unpredictable nature of financial markets.
A recent study has proposed a novel approach to modeling stock returns, using variance mixtures of normals (VMON) and negative binomial distributions to describe the distribution of daily returns. The idea is that by incorporating these non-Gaussian distributions into the model, researchers can better capture the extreme events that often drive market behavior.
The VMON approach, which has been used in various fields such as physics and finance, assumes that the logarithmic returns of stock prices follow a specific type of normal distribution known as a q-Gaussian. This distribution is characterized by a parameter q, which controls the amount of heavy-tailedness in the data. By estimating this parameter, researchers can determine how well the VMON model fits the observed data.
The negative binomial distribution, on the other hand, is used to model the counts of extreme returns, or outliers. This distribution assumes that these events occur randomly and independently, with a Poisson process governing the number of jumps in the stock price. By combining the VMON and negative binomial distributions, researchers can create a more comprehensive model of stock market behavior.
The study also proposes a generalized jump-diffusion model, which incorporates both the VMON and negative binomial distributions into a single framework. This model allows for the simulation of stock prices over time, taking into account the random fluctuations and extreme events that occur in financial markets.
To test the accuracy of this new approach, researchers compared the simulated stock prices with actual market data from the S&P 500 index. The results showed that the generalized jump-diffusion model performed well, accurately capturing the volatility and skewness of the observed data.
The implications of this research are significant, as it could lead to more accurate predictions of stock market behavior and improved risk management strategies for investors. By better understanding the underlying mechanisms driving financial markets, researchers can develop more effective models that take into account the complexities and uncertainties of the real world.
In addition, this study highlights the potential benefits of interdisciplinary research, combining concepts from physics, mathematics, and finance to tackle complex problems. As researchers continue to explore new approaches to modeling financial markets, we may uncover even more innovative solutions that can improve our understanding of these complex systems.
Cite this article: “Quantifying Market Volatility with Non-Gaussian Models: A Novel Approach to Option Pricing”, The Science Archive, 2025.
Stock Market Behavior, Financial Markets, Variance Mixtures Of Normals, Vmon, Q-Gaussian Distribution, Negative Binomial Distribution, Jump-Diffusion Model, S&P 500 Index, Risk Management, Finance And Physics.
Reference: Xinxin Jiang, “Modeling Stock Return Distributions and Pricing Options” (2025).
