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xVA Modeling: Squeezing accuracy from the industry standard Hull White model
14 August 2020
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.
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