Automatic Adjoint Differentiation, An Implementation with local volatility models

Specialeforsvar ved Christian Peter Kjær og Ulrich Drachmann

Titel:Automatic Adjoint Differentiation,  An implementation with local volatility models

Abstract: In this thesis the Automatic Adjoint Differentiation algorithm is presented in a simple manner and implemented in C++. The algorithm computes sensitivities through an application of the chain rule combined with the exibility of C++. The computational speed of AAD is compared to the well known bump-and-revalue approach, showing how vast time reductions can be achieved under local volatility models.
The thesis is divided into three parts. First part covers the theory behind Adjoint Differen-tiation and is explained through simple examples . The second part covers the different components that builds a tape-based AAD library. And the final part covers implementation of AAD for Monte Carlo simulations under a local volatility model. We present the results, and  describe how AAD allows for vast improvements in comparison to traditional methods when obtaining sensitivities providing the same accuracy.



Vejleder:  Rolf Poulsen
Censor:    Elisa Nicolato, Aarhus Universitet