# A data-driven approach for modeling the behavior of stock prices

**Authors:** Khalid Aram  
**arXiv:** [2208.02949](https://arxiv.org/abs/2208.02949)  
**Date:** 2022-08-05  
**Summary page:** https://www.summarizepaper.com/en/paper/2208.02949v1/

## Key points

- The paper presents a data-driven approach for modeling stock prices using two different approaches
- Approach 1 considers the probability distribution of day-to-day price differences, while approach 2 models the movement of the price as a stochastic birth-death process
- Historical opening prices of Apple Inc. were used to demonstrate both approaches and simulated prices from each model were compared to actual prices using information theory metrics
- Both models had information entropy and mutual information (MI) close to those of the actual data, with slightly higher entropy values for both models and slightly lower MI values than the actual data
- Model 1 attempted to mimic historical trends by generating prices using the underlying distribution of day-to-day price moves, while model 2 captured more details of the process of price movement using a birth-death stochastic process
- Model 2 produced more similar prices to the actual prices for the selected stock data and closely resembled actual price moves distribution
- This study provides valuable insights into modeling stock prices using data-driven approaches with important implications for investors seeking to understand stock market behavior and make informed investment decisions based on accurate modeling techniques.

## Summary

This paper presents a data-driven approach for modeling the behavior of stock prices using two different approaches. The first approach considers the underlying probability distribution of day-to-day price differences, while the second approach models the movement of the price as a stochastic birth-death process. Historical opening prices of Apple Inc. were used to demonstrate both approaches, and simulated prices from each model were compared to actual prices using information theory metrics. The results showed that both models had information entropy and mutual information (MI) close to those of the actual data, with slightly higher entropy values for both models and slightly lower MI values than the actual data. Model 1 attempted to mimic historical trends by generating prices using the underlying distribution of day-to-day price moves, while model 2 captured more details of the process of price movement using a birth-death stochastic process. Overall, model 2 produced more similar prices to the actual prices for the selected stock data. Furthermore, MI was calculated between the actual price moves distribution and those generated by each model, with model 2 producing price moves that closely resembled those of the actual data. In conclusion, this study provides valuable insights into modeling stock prices using data-driven approaches. Both models demonstrated good performance in providing information about actual stock prices, with model 2 capturing more details and producing more similar prices to historical trends. This research has important implications for investors seeking to understand stock market behavior and make informed investment decisions based on accurate modeling techniques.