The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Estimating security price derivatives using simulation
Management Science
Sensitivity estimates from characteristic functions
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
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Assuming the underlying assets follow a Variance-Gamma (VG) process, we consider the problem of estimating sensitivities such as the Greeks on a basket of stocks when Monte Carlo simulation is employed. We focus on a class of derivatives called mountain range options, comparing indirect methods (finite difference techniques such as forward differences) and two direct methods: infinitesimal perturbation analysis (IPA) and the likelihood ratio (LR) method, where the latter is also implemented via a recently proposed numerical technique developed by Glasserman and Liu (2007) using the characteristic function. We carry out numerical simulation experiments to evaluate the efficiency of the different estimators and discuss the strengths and weakness of each method.