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

TL;DR

This paper analyzes the correlation structure of the two-factor Hull-White interest rate model, crucial for accurate CVA calculations, revealing conditions under which the model effectively captures yield curve de-correlation.

Contribution

It provides a detailed analysis of the correlation structure in the two-factor Hull-White model, which was previously underexplored, using approximation formulas and Monte Carlo simulations.

Findings

The model captures yield curve de-correlation under specific parameter conditions.

Correlation of co-initial swap rates is characterized.

Effective for CVA modeling when parameters satisfy certain relationships.

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.