Sorry can’t give you a reference. I wrote code a few years ago to look at this effect. I found that code and here is one figure I plotted. This is based on real stock price data for QCOM stock price 1999 through 2005. In this figure, I am looking at stock prices about 36 days apart.
Stock price volatility from data. The random variable is log(P2/P1), the log of the later price to the earlier price. In this plot, P2 occurs 0.1 years after P1. A histogram is plotted with a logarithmic axis for the histogram count. A gaussian (bell curve) is fitted to the histogram, with a logarithmic y-axis, a gaussian is just a parabola. You can see the fit is great, except for some outliers on the positive side. Some of these outliers are quite a lot higher than the fitted gaussian, these are events that occur MANY TIMES more often that a log-normal distribution would suggest.
Sorry can’t give you a reference. I wrote code a few years ago to look at this effect. I found that code and here is one figure I plotted. This is based on real stock price data for QCOM stock price 1999 through 2005. In this figure, I am looking at stock prices about 36 days apart.
Thanks, that’s very useful!