  Since the introduction of the Black-Scholes model stochastic processes have
played an increasingly important role in mathematical finance. In many cases
prices, volatility and other quantities can be modeled using stochastic
ordinary differential equations. Available methods for solving such equations
have until recently been markedly inferior to analogous methods for
deterministic ordinary differential equations. Recently, a number of methods
which employ variable stepsizes to control local error have been developed
which appear to offer greatly improved speed and accuracy. Here we conduct a
comparative study of the performance of these algorithms for problems taken
from the mathematical finance literature.
