Why Stock Price Models Commonly Use Lognormal Distributions

Summary

The response addresses which probability distribution is suitable for modeling stock prices. It points to the lognormal distribution as a common model for prices, in contrast to treating the price itself as normally distributed. This reflects a modeling distinction between price levels and changes: a normal model can allow negative prices, while a lognormal model restricts prices to positive values.

The answer is brief and does not derive the distribution, estimate parameters, or address the question’s stated bounds on daily price moves. It also cautions against interpreting a lognormal price model as proof that today’s price mechanically depends on yesterday’s. The cited explanation is a starting point for distributional modeling, not evidence that lognormality captures actual stock returns or bounded price movements in every setting.

Key ideas

• Stock price levels are commonly modeled with a lognormal distribution rather than a normal distribution.
• A lognormal model keeps modeled prices positive.
• Using a lognormal distribution does not by itself establish a specific dependence of current price on the previous price.
• The brief answer does not resolve bounded daily price changes or validate the model empirically.

Tags

# Probability distribution and Stock Price Movement


# Probability distribution and Stock Price Movement












How can we use normal distribution for finding the probability of a stock price offer where current price offer depends upon the last price offer. The price offer on some day can go 10% above (at the maximum) or 10% below (at the minimum) from the last price offer. If NOT, which is the suitable distribution for the stated problem?

## Answer by rocinante (score 1)

https://quant.stackexchange.com/a/15999

Stock prices have been modeled using the Lognormal distribution, not the Normal distribution. See this paper http://math.ucsd.edu/~msharpe/stockgrowth.pdf for more detailed information.

This does not mean that the current price offer depends on the last price offer.

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