Abstract
The evaluations done by a program at runtime can be modeled by computational Directed Acyclic Graphs (DAGs) at various abstraction levels. Applying the multivariate chain rule on those computationa...
Highlights
Derivatives are fundamental in many numerical activities, from physics to economics, to predict an evolution, speed up a computation or help to make a decision
Implementation We describe a Coarse Grain Automatic Differentiation (CGAD) implementation written in Java, that satisfies the constraints on computational Directed Acyclic Graphs (DAGs) and total derivatives computation of Section 5.1
The corresponding runtime high-level domain model computational DAG is represented in Figure 16 where the 25 nodes are colored according to the module to which they belong
Summary
Derivatives are fundamental in many numerical activities, from physics to economics, to predict an evolution, speed up a computation or help to make a decision. The total derivatives of instrument prices with respect to their underlying parameters are called Greeks. They are instrumental for risk management and highly desirable for the quick Taylor approximation of prices when underlying parameters change (either in response to real-time feed events or simulation scenarios). Every classical methods for calculating derivatives in software comes with its own drawbacks. To make matters worse, those drawbacks get magnified when computing secondorder derivatives. Choosing one differentiation method is usually a trade-off between responding to user experience concerns (precision, speed) and responding to software engineering concerns (decoupling, integrability ...)
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