Abstracts

We use an example for motivation: Consider the pricing of a simple European option. The underlying SDE is easily solved by Monte Carlo. Alternatively, the corresponding PDE can be discretized using finite differences in time and space followed, for example, by a Crank-Nicholson iteration. Our reference implementation prices the option on a 360 x 1000 mesh for free parameters including the constant interest rate, strike, price of the underlying at maturity, and 138 parameters of the local volatility surface (e.g. implied volatilities) in 2 seconds on the reference computer. Bumping delivers central finite difference approximations of the 141 gradient entries after 70 seconds with full compiler optimization enabled. Our adjoint solution based on dco/c++ computes the same gradient in only 4 seconds – a speedup of almost 20.
This talk introduces algorithmic differentiation and dco/c++ including challenges and pitfalls of the general methodology. The material is based on one-day workshops presented at the ICBI Global Derivatives meetings in Chicago (11/13) and Amsterdam (04/14). Additionally, we discuss recent progress in adjoint methods on GPUs.