We construct “Hybrid Value at Risk” (HYVAR) that is an arbitrary mixture of Historical VAR and Monte Carlo VAR. The procedure is capable of retaining both the correlation matrix of the original time series and also jumps/‘fat tails'. For this reason HYVAR provides more realistic scenarios,...

A common scenario risk analysis employs a multiple factor model with assumed changes in the factors to obtain changes in non-factor variables. This analysis is sometimes designated as a “predictive stress scenario”. We choose to designate the factor model as a multifactor “CAPM” model,...

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...

Calculating risk measures can be extremely time consuming for large portfolios. Monte Carlo and historical value at risk and expected shortfall calculations can require repricing 1,000s of positions 1,000s of times. This makes risk calculations extremely challenging when the pricing functions...

This paper contains new results for helping to understand financial crises. First, we present a new model for obtaining the probability of equity crises within one year in advance, and we test it. Second and separately, various markets already in crises appear quantitatively related to a theory...