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.
FREE WHITE PAPER
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:
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.