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Two-Factor Hull-White Model Revisited: Correlation Structure for Two-Factor Interest Rate Model in CVA Calculation

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  • Osamu Tsuchiya

Abstract

The development of credit valuation adjustment (CVA) (valuation adjustments [XVA]) [Green] has increased the importance of simple interest rate models such as the Hull-White model [Tan14] [Tsuchiya]. This is because the XVA model is an FX hybrid model, and is tractable only when the interest rate part is a simple Gaussian model. For the XVA calculation of interest rate instruments, de-correlation of the yield curve can be important even for the swap portfolio. Capturing the correlation structure in the two-factor Hull-White model is an integral element of CVA (XVA) modeling. However, the correlation structure in two-factor Hull-White model has not studied enough except for the analysis in [AndersenPiterbarg]. In this study, the correlation structure of the two-factor Hull-White model is analyzed in detail. The correlation structure of co-initial swap rates is investigated using a combination of the approximation formula and Monte-Carlo simulation. The Hull-White model captures the de-correlation of the yield curve only when the parameters (volatilities and mean reversion strength) satisfy certain relationships, making the valuation of XVA by two-factor Hull-White model effective.

Suggested Citation

  • Osamu Tsuchiya, 2026. "Two-Factor Hull-White Model Revisited: Correlation Structure for Two-Factor Interest Rate Model in CVA Calculation," Papers 2603.20243, arXiv.org.
    • Handle: RePEc:arx:papers:2603.20243
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    File URL: http://arxiv.org/pdf/2603.20243
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