The Future of Financial Analytics

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Universal Algorithmic Differentiation™ revolutionizes hedging analytics

This paper focuses on the problem of computing first-order exposure, which is of primary application to hedging. It introduces a new approach, which displays a number of advantages over existing methods in the literature—Exposure Projection. In addition it demonstrates a complete implementation of Exposure Projection called Universal Algorithmic Differentiation™, within FINCAD's F3 Platform—a modern analytics platform whose architecture represents a distillation of the accumulated wisdom of over two decades of sell-side analytics platform development.

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Excerpt

In contrast to this brute-force approach [curve bumping] to exposure calculation, it is possible to compute exactly, at a computational cost that is essentially constant with respect to the number of risk factors, by applying the chain rule of differential calculus. This represents a significant advance over the bump-and-grind status quo, resulting in many cases in several orders of magnitude of computational speedup. Methods for implementing the chain rule are being popularized at the moment, under the umbrella of Automatic Differentiation (AD). While new to many, AD itself is decades old and a number of examples of such analytic exposure calculations are available in the academic literature. However, these methods suffer from a variety of drawbacks, including:

  • The set of risk factors to which exposure is calculated, and therefore the size of that set, must be known in advance.

  • The set of risk factors that can be handled is rather small.

  • Implementations cover special cases. The academic financial engineering literature provides some ideas and techniques, along with some prototype implementations. Within industry, implementations do exist in production systems, but only for some trades in some areas of some institutions.

  • Software tools attempt to add analytic exposure computation to existing code, rather than designing it in from the start, resulting in missed opportunities for optimization.

  • Potentially troublesome storage requirements for the intermediate variables used in the calculation.

In contrast, Exposure Projection (EP) gives the relevant set of risk factors as an output for essentially any derivative or portfolio, in any supported valuation approach, whether Monte Carlo simulation, closed-form, or backward-propagation in Fourier space (Cherubini (2010)). EP was designed into F3 from the start, resulting in a mature, stable, comprehensive and efficient platform for analytic risk computations that is unique among analytics vendors and, to the best of our knowledge, unparalleled by any analytics platform on the planet.