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

Paper: arXiv 2603.20243

Authors: 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.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a detailed mathematical derivation of the co-initial swap rate correlation structure in a two-factor Hull-White model, establishing specific parameter regions for yield curve de-correlation. However, empirical testing on actual market data is absent, relying primarily on synthetic Monte Carlo simulations and approximations.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Correlation Structure in 2-Factor Hull-White Model for CVA/XVA] --> B[Inputs: Model Parameters & Co-Initial Swap Rates]
    B --> C[Methodology: Combine Approximation Formula & Monte-Carlo Simulation]
    C --> D[Process: Compute Yield Curve De-Correlation & Swap Rate Correlations]
    D --> E[Outcome: Yield Curve De-Correlation Requires Specific Volatility & Mean Reversion Relationships]
    E --> F[Conclusion: Enables Effective XVA Valuation in Hybrid Models]