Presentation Abstracts

Efficient Valuation of Complex Derivatives on the GPU

Dr. Andreas Binder
MathConsult GmbH

In the pricing and risk analysis of structured financial instruments, numerical methods for the valuation, as well as for calibration of the model parameters, have to be implemented very carefully. The calibration often leads to optimization problems for which local algorithms do not converge. We present an efficient hybrid global/local algorithm and compare them to global optimization.

The latest advances of an implementation on NVIDIA Tesla machines in the UnRisk/Mathematica framework and reasons why it delivers very fast results for various advanced volatility models will be shown, as well as reasons why combining advanced technologies accelerates a calibration task that requires one million single valuations from eight hours to eight seconds.

Advanced Computational Tools for Finance Using Mathematica

Michael Kelly
Wolfram Research

Significant profits in finance are determined by the power, scope, ease, and speed of the computational toolset available. Mathematica has built upon its world-famous suite of mathematical, statistical, and computational functions to deliver a new range of financial capability. Whether it is the evaluation of bonds, cashflows, annuities, or derivatives or the estimation of underlying distributions, Mathematica has a diverse suite of functions to determine prices with ease and flexibility. This is complemented by inbuilt access to online financial data and interactive trading charts with 100 technical indicators. Ease and flexibility of coding are assured through the use of pattern matching, which allows the user to specify the structure of the financial phenomena that he is pricing. Lastly, the ability to generate standalone C code, parallelization, and high-level GPU programming make Mathematica an optimal environment for the efficient design of the fastest pricing routines.