On the Hull-White model with volatility smile for Valuation Adjustments
arxiv(2024)
摘要
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.
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