Exact simulation schemes under the Heston stochastic volatility model (e.g.,
Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive Bessel
function evaluations. We propose a new exact simulation scheme without the
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 low-bias and time
discretization schemes, which are suitable for 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.