Download pdf - CVA at Scale with Adjoint Sensitivities Xi-FINTIQ · CVA is calculated per netting set, and sensitivities with respect to market instruments are computed using adjoint AD. The resulting

Xi-FINTIQCVA at Scale with Adjoint Sensitivities

Combining the NAG Library with dco/c++ and Origami

Justin Ware, Jacques du Toit, Viktor Mosenkis and Ian Hotchkiss

Performance Challenge of XVACalculating XVA in a timely manner poses a big performance challengefor financial institutions. The number of trades encompasses the entireinstitution, not just an individual desk’s book(s). It is needed intradayas positions and markets update.

ToolsPractitioners use many tools to achieve the performance required todeliver XVA on time. Some of the most popular are:

Numerical Software Financial modelling typically uses sophisticatednumerical software. Here quality (through rigorous testing) and per-formance are key.

Algorithmic Differentiation (AD) The sensitivities of XVA risk mea-sures to market instruments are often required when reporting re-sults. Estimating these numerically can be very expensive. Algorith-mic differentiation, in particular adjoint algorithmic differentiation,offers a more accurate and computationally cheaper alternative.

Grid / Cloud XVA calculations have stages that are highly data paral-lel and computationally intensive. These can be split into multipletasks which are run on in-house grids and/or public clouds.

The Importance of DAGsDirected Acyclic Graphs (DAGs) have proven extremely useful in HPC

• They are data-centric: data dependencies are explicit, meaning datamovement can be aggressively optimized.

• They describe all levels of parallelism implicitly: programmers don’thave to try and express it, which can be challenging.

• They are platform agnostic: DAGs can be run on heterogeneous sys-tems with local and remote resources, spanning CPUs and GPUs.

• They are modular: programmers focus on describing individual tasks.Interdependence between tasks describes the overall application.

The figure below shows a DAG for a large-scale adjoint CVA calcula-tion.

Origami: a DAG Execution EngineOrigami is a light-weight task execution framework which is easy touse and maintain. Users combine tasks into a DAG. Origami can ex-ecute the DAG on an ad hoc cluster of workstations on the local net-work, on a dedicated in-house grid, on production cloud, or on a hybridof all these. Origami handles all data transfers. Machines can have dif-ferent hardware, including some with GPUs. Origami reports variousstatistics including full accounting figures for hardware use on a per-task basis. The result is a flexible, high performance execution engineaimed at business productivity and transparency.

CVA DemonstratorNAG has developed a CVA demonstration code to show how our (ad-joint) numerical libraries and our AD tool dco/c++ can be combinedwith Origami to solve large scale CVA computations. Model calibra-tion to market data is in separate tasks. Trades in netting sets are valuedin separate batches. CVA is calculated per netting set, and sensitivitieswith respect to market instruments are computed using adjoint AD. Theresulting DAG has a large number of tasks with non-trivial dependen-cies (see below) which Origami can automatically process and execute.

Combining Tools

• dco/c++ is an (A)AD tool computing sensitivities of C++ codesvia operator overloading. Since it operates at the source code level,closed source 3rd party dependencies (such as the NAG Library)cause problems.

• AD-enabled (adjoint and tangent) versions of NAG Library routinesare available which interface seamlessly with dco/c++. These al-low adjoint calculations to pass through NAG Library dependencies.

• Creating an adjoint of a distributed code is straightforward.

• The entire application is run forward as normal.

• The DAG is then reversed and the dco/c++ adjoint version of eachtask is run.

• The adjoint propagates sensitivities backward through the task. Ad-joints are taken seamlessly through NAG Library routines.

• Origami handles the data movement of adjoints between tasks.

AvailabilityThese tools are available to trial. Please contact [email protected] arrange access.

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September 2018 [email protected] www.nag.com