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 paper, 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 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.

Upper and Lower I/O Bounds for Pebbling r-Pyramids

“…We then provide an algorithm to pebble − using pebbles that requires roughly half the I/O needed by previously described algorithms [8]. We also provide a lower bound that is twice the previous best known lower bound for the same problem [8]. With these improvements, one can prove that the pebbling scheme presented here does no more than twice the I/O required by an optimal pebbling scheme.…”

“…In [8] the authors derived lower bounds for memory traffic at different levels of memory hierarchy for ( ) and ( ) . The technique used in the paper is based on the concept of a -span of the DAG [3].…”

“…( ) and ( ) are sub families of this family. We then provide an algorithm to pebble − using pebbles that requires roughly half the I/O needed by previously described algorithms [8]. We also provide a lower bound that is twice the previous best known lower bound for the same problem [8].…”

On characterizing the data movement complexity of computational DAGs for parallel execution

“…Several works followed Hong & Kung's work on I/O complexity in deriving lower bounds on data accesses [2,1,18,6,5,23,24,19,20,29,13,3,4,8,28,26]. Aggarwal et al provided several lower bounds for sorting algorithms [2].…”

“…Aggarwal et al provided several lower bounds for sorting algorithms [2]. Savage [23,24] developed the notion of S-span to derive Hong-Kung style lower bounds and that model has been used in several works [19,20,26]. Irony et al [18] provided a new proof of the Hong-Kung result on I/O complexity of matrix multiplication and developed lower bounds on communication for sequential and parallel matrix multiplication.…”