In order to characterize a statistical probability distribution p(x) of a variable x, the moments of the distribution are used; the first two of which are the mean and standard deviation. The z-score is often used to characterize data points of x (e.g. outliers with large z-scores). Polynomials...

We present an exact analytic solution to the two-dimensional correlated default structural Merton model in the form of a local volatility problem using a conformal square-root transformation of the exact solution to a 2D hybrid barrier problem. We also give an approximation and evaluate it...

This is the third paper in a series devoted to obtaining noise-reduced, stable correlations by smoothing time series using Singular Spectrum Analysis, or SSA. Here we show that the SSA-based correlations are superior in terms of noise reduction, employing a number of simple tests using Random...

We introduce a methodology from geophysics, Singular Spectrum Analysis (SSA), to obtain stable, noise-cleaned correlations for long term risk (e.g. counterparty risk). SSA is applied to time series to smooth them in a robust manner. The SSA-smoothed time series are then used to obtain the...

We summarize new results for estimating correlations for use in risk management. These estimates have better behavior than traditional estimation approaches from both a business standpoint and a technical standpoint. We smooth time series using Singular Spectrum Analysis (SSA) and compute...

The DRSK public model estimates forward-looking real-world default probabilities for publicly traded firms. The model also assigns credit grades based on the estimated default probabilities. The product covers firms in all regions and sectors of operation for which the necessary data is...

The DRSK private firm model produces estimates of real-world default probabilities (DPs) for private companies. The product covers all firms for which the requisite data is available, providing point in time DP term structures for about 500,000 private firms globally.This year, we are...

Amidst the avalanche of articles on big data and machine learning, the phrase "after cleaning the data" is often found. Here we focus on the work hidden behind this phrase. We analyze the types of dirty data found in financial time series, the problems caused by dirty data, and the performance...

We present the framework for a distressed bond model. The utility is as a proxy for calculating the risk of a distressed bond portfolio. We elaborate several possible implementations and give an example

We introduce advanced idiosyncratic risk (“AI-Risk”), a parsimonious correlated residual correction to a predictive stress CAPM-like factor model, aimed to get more accurate stock-stock correlations. We find that AI-Risk can be significant for stock portfolios. Inclusion of AI-Risk gives a...