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xVA Modeling: Squeezing accuracy from the industry standard Hull White model
Market volatility induced by the COVID-19 pandemic has once again revealed the impact Valuation Adjustments (xVAs) of derivative portfolios can have on banks' earnings, as outlined in a Risk.net paper " FVA losses back in the spotlight after coronavirus stress". These xVA losses were in part caused by a rapid drop in interest rates, brought on by central banks slashing benchmarks rates to near zero. For an xVA trader to properly react and hedge the xVA book to interest rate volatility, the trader needs access to a range of xVA market sensitivities that are accurate and efficient to compute. This can be a challenging task for xVA, due to it being a portfolio level quantity that requires Monte Carlo simulation to capture the joint dependence of all risk factors on which the portfolio depends and requires revaluation of the full portfolio within the simulation to compute forward exposures. xVA computation engines therefore often require a trade-off between accuracy and speed.
While various interest rate models can be used to compute xVA, a workhorse for the xVA engine that is widely used across the industry is the single factor Hull White model. It is tractable in that it has analytic or semi-analytic formula for standard quantities like zero coupon bonds and swaptions prices, allowing for a stable and efficient calibration and simulation. However, with only a single factor per currency the number of free parameters available to fit the market term structure is limited. It is normally just a limited set of at-the-money swaption volatilities to which the model is calibrated. This raises the obvious question as to how useful the model is for xVA calculations on diverse portfolios of interest rate products of different maturities and tenors.
In a two-part paper, Christoph Puetter and Stefano Renzitti of IHS Markit's Financial Risk Analytics group explore the extent to which you can squeeze accuracy out of the single factor Hull White for xVA simulation. In the first part, they investigate the optimum selection of at-the-money volatility to use for calibration. Calibrating to a diagonal of coterminal swaptions is common to price Bermudan swaptions. However, when it comes to xVA exposure simulation, they find that a Chevron shape selection of swaptions can be superior when the goal is to use a single calibration to generate exposures of swaps with varying maturities. The intuition being to match the peak exposure of the different length swaps.
The second paper explores the important impact of the short rate mean reversion. This is a free parameter that they find to be critical to getting the model to accurately capture the portion of the swaption volatility surface to which the model was not directly calibrated. A sloppy selection of this parameter leads to significant pricing errors, whereas a careful calibration of the mean reversion allows for a vastly superior model. Interestingly, in the currently low interest rate environment, it is a negative mean reversion that best fits the swaption surface.
Finally, the authors illustrate how their proposed calibration techniques lead to a model that is more stable and able to react to the market volatility of the COVID-19 turmoil through the early part of 2020.
xVA modeling will continue to be a trade-off between accuracy and efficiency. But with some careful calibrations of your models, you may be able to squeeze out accuracy where you didn't expect it. Full details of the analysis carried out by IHS Markit's quantitative team can be found by downloading the papers below.
- HWXF Calibration And CVA Part I Instrument Calibration
- HWXF Calibration And CVA Part II Mean Reversion Optimization
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