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 Lévy-driven underlyings and to finding sensitivities of performance measures in queueing systems. The numerical results demonstrate the efficacy and speed of the method.
- Acceptance-rejection sampling
- Monte Carlo simulation
- Option pricing under Levy processes
- Queuing theory
- Sensitivity analysis