Application of Normal Distribution to Stock Exchange and Binomial Tree Model

Abstract

Stock price modeling is a cornerstone of financial economics, in which a correct representation of price behavior is critical to asset pricing and risk management. This paper aims at discussing the use of the lognormal distribution in stock price models and provides the aim of elucidating its use in both discrete-time and continuous-time models. The study employs a probabilistic modeling methodology that involves theoretical study and introduces a geometric Brownian motion as the stochastic behavior of the stock prices. The work studies how the changes in the stock prices can be modeled as a multiplicative process over time by investigating the characteristics of lognormal distribution. The findings show that the stock prices are lognormally distributed, given the usual modeling assumptions, which assure of stock prices being non-negative and reflecting observed market behavior. Additionally, the discussion shows that the geometric Brownian motion is a sound theoretical basis of popular financial models. To sum up, it is necessary to state that the paper proves the usefulness and feasibility of the use of lognormal distribution in the financial models, especially in the valuation of assets and options.