We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence homology to detect and quantify topological patterns that...

We consider an extension of the variance-gamma process implying that the linear drift rate of the process can switch suddenly by a jump. The value of jump is modeled by the multidimensional distribution, the jump time is simulated by the exponential distribution. Together with the simplest...

The recent financial crisis has accentuated the fact that extreme outcomes have been overlooked and not dealt with adequately. While extreme value theories have existed for a long time, the multivariate variant is difficult to handle in the financial markets due to the prevalent...

This paper provides an early warning indicator for bubbles in financial markets. The indicator is based on traditional unit root tests, more precisely on the augmented Dickey-Fuller test and may be used in a repeated manner with rolling samples. The performance of the indicator is tested...

Persistent variations in the log price-to-dividend ratio (PtDR) have triggered a lively discussion in the literature. This paper proposes a present value model incorporating this persistence through a time-varying steady state of the PtDR. Log-likelihood statistics confirm that the time-varying...