An exact method for the sensitivity analysis of systems simulated by rejection techniques

• Ways of computing sensitivities for acceptance–rejection simulation are introduced.
• We use minimal measure changes to prevent changes in rejection decisions.
• We develop low-variance estimators for Greeks in Levy process models.
• We also look at applications to performance measures for queuing systems.
• Extensive numerical results are presented.

We compute first- and second-order sensitivities of functions simulated by rejection techniques. The methodology is to perform a measure change on every acceptance test, so that the pathwise discontinuities resulting from the rejection decisions are removed. The change of measure is chosen to be optimal in terms of minimizing variances of the likelihood ratio terms. Applications are presented for computing Greeks of equity options with certain Le´vy-driven underlyings and to finding sensitivities of performance measures in queueing systems. The numerical results demonstrate the efficacy and speed of the method.