We study the relationships between the mean of functional L^p-norms of persistence topological landscapes of noisy datasets and statistical properties of the underlying probability distributions. We establish a functional relationship of the average L^p-norms to variability of datasets sampled...

We apply the novel econometric method – the time-resolved topological data analysis - to detect approaching market instabilities in multiple sectors of North American economy. Using the Takens' embedding and the sliding window's technique, we detect transient loops that appear in a topological...

We analyze four major cryptocurrencies (Bitcoin, Ethereum, Litecoin, and Ripple) before the digital asset market crash at the beginning of 2018. We also analyze Bitcoin before some of the mini-crashes that occurred during the period 2016 - 2018. All relevant time series exhibited a highly...

The q-Gaussian generalization of the Merton framework allows pricing of the additional risk premium related to fluctuations of the variance of the market value of a company's assets, which can explain the observed level of short-term CDS spreads of investment grade issuers. The derived simple...

In this paper we derive the closed-form expression for the term structure of CDS spreads with the stochastic variance risk being priced. The resulting CDS spreads are determined by the proximity of the default point as well as the realized distribution of the inverse variance of the issuer's...

We present the non-Gaussian extension of the traditional Merton framework, which takes into account slowly relaxing fluctuations of the volatility of the firm's market value of financial assets. The minimal version of the model depends on the Tsallis entropic parameter q and the generalized...

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...

If stochastic perturbation of the long-term discount factor by random shocks in instantaneous interest or consumption growth rates is weak, the approximate model-independent description of an effective discount rate is possible in terms of first and second cumulants of these processes. The...

Fat tails of q-Gaussian distributions of daily log-leverage-returns of 520 North American industrial firms reported by Katz and Tian (2013) imply a significantly higher credit risk at short time-horizons and/or large initial distances to the default barrier than forecasted by traditional...

We study the probability distributions of daily leverage returns of 520 North American industrial companies that survive de-listing during the financial crisis, 2006-2012. We provide evidence that distributions of unbiased leverage returns of all individual firms belong to the class of...