On Comparing Financial Option Price Solvers on FPGA

A number of different numerical methods for accelerating financial option pricing using FPGAs have recently been investigated, such as Monte-Carlo, finite-difference, quadrature, and binomial trees. However, these papers only compare acceleration of each method against the same method in software, and do not consider a more important practical question, which is to identify the method that provides the best FPGA performance for a given option pricing application, regardless of raw speed-up over software. This paper proposes a framework for comparing the performance of numerical option pricing methods using FPGAs, taking into account both speed (time to solution) and accuracy (quality of solution), and examines how the speed-accuracy trade-off curve varies for each method. We apply the framework to European and American option pricing problems using Virtex-4 parts, and show that the quadrature solver converges fastest for both European and American options, and is also the most accurate in terms of root mean squared error for European options. However, when very accurate American results are needed the finite-difference solver is the most efficient method. Our results also show that the Monte-Carlo solver is at least 100 times less accurate in log scale than those based on other pricing methodologies, this drawback outweighs its benefit of having large raw speed-ups found in previous papers.