Architecture independent parallel binomial tree option price valuations

We introduce an architecture independent approach in describing how computations such as those involved in American or European-style option valuations can be performed in parallel in the binomial-tree model. In particular we present an algorithm for the multiplicative binomial tree option-pricing model that can also be directly generalized to the general additive binomial tree model. The algorithm is described and analyzed in an architecture independent setting and running time and performance characteristics are expressed in terms of problem size n, which is the time horizon, and the parameters p, L and g of the bulk-synchronous parallel model of computation. In particular, our algorithm achieves optimal theoretical speedup O(p) and is thus within a 1 + o(1) multiplicative factor of the corresponding sequential method. In order to verify the practicality of the introduced algorithm an experimental study of an implementation of the algorithm on a PC cluster is also presented; the implementation works with only recompilation of the source code under two popular programming libraries MPI (LAM-MPI) and BSPlib and is thus not only architecture but also communication library independent.