Cache-optimal algorithms for option pricing

Abstract

Today computers have several levels of memory hierarchy. To obtain good performance on these processors it is necessary to design algorithms that minimize I/O traffic to slower memories in the hierarchy. In this article, we study the computation of option pricing using the binomial and trinomial models on processors with a multilevel memory hierarchy. We derive lower bounds on memory traffic between different levels of the hierarchy for these two models. We also develop algorithms for the binomial and trinomial models that have near-optimal memory traffic between levels. We have implemented these algorithms on an UltraSparc IIIi processor with a 4-level of memory hierarchy and demonstrated that our algorithms outperform algorithms without cache blocking by a factor of up to 5 and operate at 70% of peak performance.