This paper presents a subordinated stochastic process model with finite variance for speculative prices, developed by Peter King Clark. The model addresses the empirical observation that price changes in speculative markets are not normally distributed, leading to leptokurtic (heavy-tailed) distributions. The model is based on the idea that price changes are subordinate to a normal distribution, meaning they are influenced by a random process that determines the number of independent increments contributing to each price change. The paper discusses the limitations of the standard Central Limit Theorem in explaining price changes, as the increments in speculative price processes do not meet the necessary conditions for normality. Instead, the model proposes that the distribution of price changes is stable, with finite variance, and is derived from a subordinated stochastic process. This process involves a directing process that determines the number of increments contributing to each price change. The paper also presents tests of the model using data on cotton futures prices. It shows that the distribution of price changes can be approximated by a lognormal-normal distribution, which has a finite variance and exhibits leptokurtic characteristics. The model is tested against stable distributions, and the results indicate that the lognormal-normal distribution provides a better fit to the observed data. The paper concludes that the finite-variance subordination model is a good approximation of the true distribution of price changes in speculative markets. The model accounts for the observed leptokurtic distribution of price changes and provides a framework for understanding the behavior of speculative prices over time. The model is supported by empirical evidence and theoretical considerations, and it offers a more accurate description of price changes than the standard normal distribution.This paper presents a subordinated stochastic process model with finite variance for speculative prices, developed by Peter King Clark. The model addresses the empirical observation that price changes in speculative markets are not normally distributed, leading to leptokurtic (heavy-tailed) distributions. The model is based on the idea that price changes are subordinate to a normal distribution, meaning they are influenced by a random process that determines the number of independent increments contributing to each price change. The paper discusses the limitations of the standard Central Limit Theorem in explaining price changes, as the increments in speculative price processes do not meet the necessary conditions for normality. Instead, the model proposes that the distribution of price changes is stable, with finite variance, and is derived from a subordinated stochastic process. This process involves a directing process that determines the number of increments contributing to each price change. The paper also presents tests of the model using data on cotton futures prices. It shows that the distribution of price changes can be approximated by a lognormal-normal distribution, which has a finite variance and exhibits leptokurtic characteristics. The model is tested against stable distributions, and the results indicate that the lognormal-normal distribution provides a better fit to the observed data. The paper concludes that the finite-variance subordination model is a good approximation of the true distribution of price changes in speculative markets. The model accounts for the observed leptokurtic distribution of price changes and provides a framework for understanding the behavior of speculative prices over time. The model is supported by empirical evidence and theoretical considerations, and it offers a more accurate description of price changes than the standard normal distribution.