RESUMO
Using the multifractional Brownian motion as a model of the price dynamics, we analyze the impact of the COVID-19 pandemic on the efficiency of fifteen financial markets from Europe, US and Asia. We find that Asian markets (Hang Seng, Nikkei 225, Kospi) have recovered full efficiency, while European and US markets - after an initial rebound - have not yet returned to the pre-crisis level of efficiency. The inefficiency that currently characterizes US and European markets originates moderately high levels of volatility.
RESUMO
The recent global financial crisis has threatened the financial system with total collapse of many economic sectors with a particular penetration to world's stock markets. The large swings in the prices of international stocks or indexes have reinvigorated the debate on their mathematical modeling. The traditional approaches do not seem to be very exhaustive and satisfactory, especially when extreme events occur. We propose a fractal-based approach to model the actual prices by assuming that they follow a Multifractional Process with Random Exponent. An empirical evidence is offered that this stochastic process is able to provide an appropriate modeling of actual series in terms of goodness of fit by comparing three main stock indexes.
RESUMO
The last systemic financial crisis has reawakened the debate on the efficient nature of financial markets, traditionally described as semimartingales. The standard approaches to endow the general notion of efficiency of an empirical content turned out to be somewhat inconclusive and misleading. We propose a topological-based approach to quantify the informational efficiency of a financial time series. The idea is to measure the efficiency by means of the pointwise regularity of a (stochastic) function, given that the signature of a martingale is that its pointwise regularity equals 12. We provide estimates for real financial time series and investigate their (in)efficient behavior by comparing three main stock indexes.