10/1/16: Tsallis Entropy: Do the Market Size and Liquidity Matter?

Updated version of our paper:
Gurdgiev, Constantin and Harte, Gerard, Tsallis Entropy: Do the Market Size and Liquidity Matter? (January 10, 2016), is now available at SSRN: http://ssrn.com/abstract=2507977.

Abstract:      
One of the key assumptions in financial markets analysis is that of normally distributed returns and market efficiency. Both of these assumptions have been extensively challenged in the literature. In the present paper, we examine returns for a number of FTSE 100 and AIM stocks and indices based on maximising the Tsallis entropy. This framework allows us to show how the distributions evolve and scale over time. Classical theory dictates that if markets are efficient then the time variant parameter of the Tsallis distribution should scale with a power equal to 1, or normal diffusion. We find that for the majority of securities and indices examined, the Tsallis time variant parameter is scaled with super diffusion of greater than 1. We further evaluated the fractal dimensions and Hurst exponents and found that a fractal relationship exists between main equity indices and their components.

23/1/2012: Extreme Events

Going through 2 charts and mapping the big themes of the ongoing crises, one has to be in awe of the volatility. Here are the maps of extreme (3-Sigma-plus) events with 'directionality' reflected:

Lovely, aren't they? But the trick in the above is: we are not at the decay stage of volatility on the sovereigns re-pricing stage. This, to me, suggests that once the sovereign crisis re-pricing draws to conclusion (whenever that might happen - isa different story), there will be the need for finding that 'new normal' (reversion-to-the-trend target) for the markets valuations overall. And that is the whole new game, dependent less on the previous equilibrium that should have followed the Great Bursting period, but more on the future risks and trends in post-debt economies. Which, itself, really depends on whether any given market can sustain growth without endless supports (implicit and explicit) from the Government borrowings.

Just thought I'd throw few thoughts out there...