Algorithmic Differentiation (AD) for Computational Finance: Introduction

Presenter: Uwe Naumann: The Numerical Algorithms Group Ltd. (NAG)

Session 1. Running Time: 1hr 28mins

Session 2. Running Time: 47mins

Session 2a. Running Time: 1hr 10mins

Session 3. Running Time: 1hr 32mins

Session 4. Running Time: 1hr 9mins

Prerequisites

• You are interested in accurate and cheap greeks

• You are unhappy with the accuracy and/or the computational cost of bumping

Outline

Motivation. Tangent and Adjoint AD

• motivation: accurate and cheap greeks

                 –   hello world of finance: race

• first- and higher-order tangent and adjoint AD

                 –   tangents (directional derivatives) and adjoints

                 –   associativity of chain rule of differential calculus

                 –   drivers

                 –   second-order tangents and adjoints

                 –   recursion for higher order

• exercise

Tangent and Adjoint Code by AD (Part I)

• tangent code

                 –   tangent code generation rules

                 –   example (live)

                 –   tangent code by overloading

                 –   second- and higher-order tangent code

• adjoint straight-line code

                 –   adjoint code generation rules

                 –   example (live)

• exercise

Tangent and Adjoint Code by AD (Part II)

• intraprocedural adjoint code

                 –   control flow reversal

                 –   example (live)

• interprocedural adjoint code

                 –   split call reversal

                 –   example (live)

• adjoint code by overloading

• second- and higher-order adjoint code

• exercise

Advanced Topics in AD. Outlook

• checkpointing adjoint code

• (symbolic) tangents and adjoints of numerical methods

• coupling with bumping

• “mind the gap”

• software tool support

• conclusion and outlook

Reading

• U. Naumann: The Art of Differentiating Computer Programs, An Intro-duction to Algorithmic Differentiation, SIAM, 2012. http://www.siam.org/books/se24