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...

Stock prices are well known to exhibit behaviors that are difficult to model mathematically. Individual stocks are observed to exhibit short term price reversals and long term momentum, while their industries only exhibit momentum. Here we show that individual stocks can be modeled by simple...

Despite the recent market upheavals, the OTC derivatives markets continue to comprise one of the largest components of the financial markets, with an overall outstanding notional of $547 trillion in December 2008, 70% of which are in interest rate derivatives. As of June 2009, this grew to $605...

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 Bloomberg sovereign risk function (SRSK) provides quantitative estimates of a sovereign entity's default probability (DP) term structure.The SRSK model was last updated in June 2017. This year we have reviewed and revised the model. This white paper documents the newly updated DP model and...

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...

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...