  Exact simulation schemes under the Heston stochastic volatility model (e.g.,
Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive modified
Bessel function evaluations. We propose a new exact simulation scheme without
the modified Bessel function, based on the observation that the conditional
integrated variance can be simplified when conditioned by the Poisson variate
used for simulating the terminal variance. Our approach also enhances the
low-bias and time discretization schemes, which are suitable for pricing
derivatives with frequent monitoring. Extensive numerical tests reveal the good
performance of the new simulation schemes in terms of accuracy, efficiency, and
reliability when compared with existing methods.
