Hybrid correlation matrices

Integrating available implied volatility data into a historical correlation matrix is an essential part of calibrating a Monte Carlo credit value adjustment pricing simulation at the portfolio level, but can yield nonsensical results. Someshwar Roy and Ersel Korusoy use principal components analysis and implied time series to ensure the output conforms to the properties of a correlation matrix

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Monte Carlo simulations for pricing are ubiquitous in finance, particularly for credit valuation adjustments, which are carried out at portfolio level. Ideally in such a situation one uses market-implied data. However, with diversified portfolios this is often impossible due to a lack of tradable instruments. The only other source of correlation data is historical but the result of mixing historical and implied correlations does