So I’ve written on the financial markets for Mint. This is not part of my usual mandate – which is to write data/quant stories related to politics and the economy and suchlike, I believe this is very different from the kind of markets pieces Mint normally writes.
For starters, I see that there is very little “quant” stuff in mainstream financial reporting. You have tonnes of writing on “fundamentals” (“Company A got this new deal so expect their stock price to increase” or “Company B has regulatory trouble, so short their stock” level) and tonnes on “technicals” (“the nifty will find resistance at 7891” and “we are seeing a head-and-shoulders market (sponsored by P&G)” type), but none on quant.
In fact, if you were to learn finance by reading the newspapers (admittedly a stupid thing to do), you wouldn’t know of how bankers work, of the models they use, of random walks, and of the Black-Scholes-Merton equation. You would think of finance as a rather boring accounting-related fundamentals or voodoo technical stuff. All the cool quant stuff will be lost to you.
So in my attempt to remedy that, I’ve gone all the way and introduced readers of Mint to Fractional Brownian Motion. No, really. I tell a story from Genesis (I actually looked up and read this chapter from the Old Testament so that I could quote it properly), and then relate it to the flooding of the Nile, and that to the work of hydrologist Harold Edwin Hurst, and how that can help us understand the markets. An extract:
Hurst was to remain in Egypt and be associated with the Nile for 62 years (the Egyptian government retained his services after the country’s independence). Looking through 847 years of Nile overflow data (existence of this data tells us much about the farsightedness of the Mameluke and Ottoman rulers of Egypt), Hurst managed to crack the puzzle. The model he built was one of long-range dependence. It is a model that has far-reaching effects, most importantly in the financial markets.
Turning this around, analysing the rescaled range of a time series as a function of number of time periods will tell us about its long-range dependence. All we need to do is to find the exponent of N, according to which the rescaled range grows. If this exponent is half (in which case the rescaled range grows with the square root of N), we have a regular random walk (or Brownian motion). If the exponent is greater than half, we have positive long-range time dependence, and the value of the exponent tells us the degree of such dependence. Similarly, if the exponent is less than half, we have negative long-range time dependence, which is known as fraction Brownian motion.