On the Hull-White model with volatility smile for Valuation Adjustments

ArXiv ID: 2403.14841 “View on arXiv”

Authors: Unknown

Abstract

Affine Diffusion dynamics are frequently used for Valuation Adjustments (xVA) calculations due to their analytic tractability. However, these models cannot capture the market-implied skew and smile, which are relevant when computing xVA metrics. Hence, additional degrees of freedom are required to capture these market features. In this paper, we address this through an SDE with state-dependent coefficients. The SDE is consistent with the convex combination of a finite number of different AD dynamics. We combine Hull-White one-factor models where one model parameter is varied. We use the Randomized AD (RAnD) technique to parameterize the combination of dynamics. We refer to our SDE with state-dependent coefficients and the RAnD parametrization of the original models as the rHW model. The rHW model allows for efficient semi-analytic calibration to European swaptions through the analytic tractability of the Hull-White dynamics. We use a regression-based Monte-Carlo simulation to calculate exposures. In this setting, we demonstrate the significant effect of skew and smile on exposures and xVAs of linear and early-exercise interest rate derivatives.

Keywords: valuation adjustments (xVA), interest rate derivatives, affine diffusion, stochastic differential equations, calibration

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats
  • Why: The paper is highly mathematical, deriving a novel SDE with state-dependent coefficients and using advanced techniques like the Fokker-Planck equation and Riccati ODEs for an affine diffusion framework, but it focuses on theoretical model construction and exposure calculation methodology rather than presenting extensive backtesting results or performance metrics on real-world data.
  flowchart TD
    Goal["Research Goal<br>Model skew & smile in IR for xVA?"]
    Method["Methodology<br>rHW Model via RAnD<br>State-dependent SDE"]
    Calib["Calibration<br>Semi-analytic to European Swaptions"]
    Sim["Computation<br>Regression-based Monte Carlo for Exposures"]
    Out["Key Findings<br>Skew/smile significantly affect<br>Exposures & xVA for IR derivatives"]