Modern Computational Finance

CHAPTER 15Acceleration with Expression Templates

In this final chapter, we rewrite the AAD library of Chapter 10 in modern C++ with the expression template technology. The application of expression templates to AAD was initially introduced in [89] as a means to accelerate AAD and approach the speed of manual AD (see Chapter 8) with the convenience of an automatic differentiation library.

The result is an overall acceleration by a factor two to three in cases of practical relevance, as measured in the numerical results of Chapters 12, 13, and 14. The acceleration applies to both single-threaded and multi-threaded instrumented code. It is also worth noting that we implemented a selective instrumentation in our simulation code of Chapter 12. It obviously follows that only the instrumented part of the code is accelerated with expression templates. It also follows that the instrumented part is accelerated by a very substantial factor, resulting in an overall acceleration by a factor two to three.

The resulting sensitivities are identical in all cases. The exact same mathematical operations are conducted, and the complexity is the same as before. The difference is a more efficient memory access resulting from smaller tapes, and the delegation of some administrative (not mathematical) work to compile time. The benefits are computational, not mathematical or algorithmic. Like in the matrix product of Chapter 1, the acceleration is nonetheless substantial.

The new AAD library exposes ...