  We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in
barrier options under the Heston (1993) stochastic volatility model. This is
done by modifying the LT method from Imai and Tan (2006) for the Heston model
such that the first uniform variable does not influence the stochastic
volatility path and then conditionally modifying its marginals to fulfill the
barrier condition(s). We show this method is unbiased and never does worse than
the unconditional algorithm. Additionally the conditioning is combined with a
root finding method to also force positive payouts. The effectiveness of this
method is shown by extensive numerical results.
