I am looked any multiple sources and tutorials which tells me that the price of a stock has a lognormal distribution. I understand that unlike stock returns, which can have both positive and negative values, stock prices are non-negative and follows a lognormal distribution.
However, I have sampled with different stock prices by plotting a histogram of their log(price) and here are the results. They do not show lognormal distribution. Am I doing something wrong?
Histogram of AAPL log(price) 1
You are right:
Lognormal distribution is not representative of stock prices. Neither is it verified by backward-looking evidence as shown in your graphs, nor it is supported by forward-looking market information, such as the stock-option prices.
It is well known that stock prices exhibit the so-called fat tails, again verifiable from historical data as well as by volatility skews/smiles observed in real-life markets. The financial market crisis of 2008 was a prime example of outsized tail movements.
Lognormal models are just the starting point in looking at stock prices. Serious market players employ more realistic distribution models, such as shifted lognormal, stochastic volatility, etc. for modeling their stock-based products.