Algorithmic Differentiation (AD) for Computational Finance

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Course Running Time: 6 Hours

£99.00

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Session 1. Running Time: 1 Hour 28 Minutes

Session 2. Running Time: 47 Minutes

Session 2a. Running Time: 1 Hour 10 Minutes

Session 3. Running Time: 1 Hour 32 Minutes

Session 4. Running Time: 1 Hour 9 Minutes

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About the Presenter

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Uwe Naumann: Professor of Computer Science, RWTH Aachen University

Uwe Naumann is the author of the popular text book on (Adjoint) Algorithmic Differentiation (AAD) titled “The Art of Differentiating Computer Programs” and published by SIAM in 2012. He holds a Ph.D. in Applied Mathematics / Scientific Computing from the Technical University Dresden, Germany.

Following post-doctoral appointments in France, the UK and the US, he has been a professor for Computer Science at RWTH Aachen University, Germany, since 2004. As a Technical Consultant for the Numerical Algorithms Group (NAG) Ltd. Uwe has been playing a leading role in the delivery of AAD software and services to a growing number of tier-1 investment banks since 2008.

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Prerequisites

• You are interested in accurate and cheap greeks
• You are unhappy with the accuracy and/or the computational cost of bumping

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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