Recent years have seen an increased level of interest in pricing equity
options under a stochastic volatility model such as the Heston model. Often,
simulating a Heston model is difficult, as a standard finite difference scheme
may lead to significant bias in the simulation result. Reducing the bias to an
acceptable level is not only challenging but computationally demanding. In this
paper we address this issue by providing an alternative simulation strategy --
one that systematically decreases the bias in the simulation. Additionally, our
methodology is adaptive and achieves the reduction in bias with "near" minimum
computational effort. We illustrate this feature with a numerical example.Comment: 23 pages, 4 Postscript figure