Podcast: Burnett and Piau on their comprehensive framework for valuation adjustments
Five years ago, the valuation adjustment (XVA) quant team at Barclays started working on a project aimed at assessing the impact of simplifying XVA models. One simplification they looked at was about treating some of the stochastic components of their models as deterministic – removing part of the ability to capture randomness and, in exchange, gaining simplicity and speed of calculation.
What started as a model risk experiment prompted by Barclays traders grew in scope and applicability until it became a comprehensive model that is now in production for the bank’s XVA calculations.
Ben Burnett, head of the XVA team, and Benji Piau, a senior quant on the same team, are the guests of this episode of Quantcast. They worked on the project with their colleague Ryan McCrickerd, an interest rate quant. Here, they talk about the path that led to building the model, which is also described in their paper, The fundamental representation of pricing adjustments.
The primary purpose of their work was to obtain an estimate of the impact of what is not modelled, hence measuring the loss of accuracy and estimating the future profit and loss (P&L) bleed that comes with simplification of the model.
As the project started, says Burnett, “Some of the things in our Monte Carlo simulation were treated as deterministic, and we wanted to know how wrong we might be by doing that.” They realised that solving that problem would provide the basis of answering the same question about other simplifications of stochastic frameworks.
The second purpose of the paper came as an unexpected development of the first – it allowed them to design a comprehensive framework for XVA pricing.
At its core, the model compares two pricing measures – the base measure and the target measure – from which a base price and a target price are calculated. The base measure is a simplified model in which deterministic variables are used in place of some stochastic ones; in essence, it shows a world in which measures are certain, and all other scenarios have zero probability. The target measure is the probabilistic representation of that world and incorporates its inherent randomness. The adjustment, accounting for the ‘bleed’, is what bridges these two prices.
The framework decomposes any adjustments into three natural parts: model, discounting and payout. Burnett and Piau explain that all previous contributions on the topic – such as those of Piterbarg, Burgard and Kjaer and Kenyon – would fall into these categories.
The second layer of the model is represented by so-called meta-adjustments – a term introduced by the Barclays team to indicate an otherwise cacophonous ‘adjustments of adjustments’, or any second-order adjustment to a standard XVA. This means the original adjustment now takes the place of the simplified base price, and another adjustment is required to account for the difference between the base and the ‘true’ target adjustment price.
Meta-adjustments would include, for example, sensitivities of one adjustment to another adjustment.
“Now we have an XVA that we hedge,” says Piau, by way of example: “What is the cost of hedging those XVAs?”
Meta-adjustments are easily derived and therefore tractable, though computing them is not straightforward, says Piau.
One attractive feature of this model is that it is designed to make the most of the calculations a desk has already computed – which is why a stochastic variable can be turned into a deterministic one. “That’s what should make this easy, at least to get an estimation – an approximation – and that was really the point of this work,” says Burnett.
Its generality allows the model to be applied to most products and portfolios. By construction, however, it does not work with American options because the mathematical architecture is not suited to capture the dynamics of callable products.
Burnett and Piau plan to develop their model further in various directions, strengthening the numerical calculation necessary for the target price, and exploring potential advantages of using artificial intelligence for the sections of the XVA engine the bank uses.
Index
00:00 Introduction
05:45 Motivation for a unified approach to XVA
07:29 P&L bleed
11:55 Model, discounting and payout components
13:22 Base price and target price
15:14 Meta-adjustments
19:25 Applicability and calculation speed
23:30 Traders, validators, quants and other potential users
26:27 Model set-up and assumptions
33:00 Future research projects
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