It details the formation and subsequent demise of Long Term Capital Management, LTCM.
An interesting read that underscores my long held belief that economists are poor mathematicians, and generally don’t know jack shit.
The basic problem is similar to the recurring problem I have with various very well educated and intelligent people relative to MH370.
Both the movement of stock value and the frequency of the MH370 oscillator strongly resemble a random walk. A random walk has the property that it is neither stationary nor ergodic. You cannot apply conventional log normal analytics to a random walk.
Stationary means that if I take statistics from any two random walks that they will converge. Not true.
Ergodicity means that if I take statistics from 20 one hour random walks they will be similar to statistics taken from one 20 hour random walk. Also not true.
We are conditioned to believe that given a set of numbers that we can compute a mean and variance that are meaningful. This is only true for stationary and ergodic processes (please Wiki stationarity and ergodicity). It would seem that people fall asleep in math class when the properties of data sets are discussed or maybe they are not discussed at all. We can take a mean and variance for any set of data. The math is trivial and well-defined. The problem is that it is often completely meaningless to do so.
The link below summarizes a post I made on this subject relative to MH370. I sent it to the ATSB (Australian search authority) and Dr. Holland readily admitted that the oscillator behavior is neither stationary nor ergodic. He did not explain why he went on to compute the mean and variance of oscillator data logged on previous flights.
So it goes with Black-Scholes. It is deeply flawed for the same reason. The process it is trying to model, stock price movement, is neither stationary nor ergodic. It simply cannot be done using log normal statistics which are the basis for the Black-Scholes model. LTCM found this out the hard way - by losing billions of dollars of other people’s money.
End of rant. I feel better now.
