Estimating security price derivatives using simulation
Management Science
An overview of derivative estimation
WSC '91 Proceedings of the 23rd conference on Winter simulation
Likelilood ratio gradient estimation: an overview
WSC '87 Proceedings of the 19th conference on Winter simulation
Probability Gradient Estimation by Set-Valued Calculus and Applications in Network Design
SIAM Journal on Optimization
Monte Carlo simulation in financial engineering
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Estimating Quantile Sensitivities
Operations Research
Probability: Theory and Examples
Probability: Theory and Examples
A reflection-based variance reduction technique for sum of random variables
Proceedings of the Winter Simulation Conference
Pathwise derivative methods on single-asset american option sensitivity estimation
Proceedings of the Winter Simulation Conference
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The Greeks are the derivatives (also known as sensitivities) of the option prices with respect to market parameters. They play an important role in financial risk management. Among many Monte Carlo methods of estimating the Greeks, the classical pathwise method requires only the pathwise information that is directly observable from simulation and is generally easier to implement than many other methods. However, the classical pathwise method is generally not applicable to the Greeks of options with discontinuous payoffs and the second-order Greeks. In this paper, we generalize the classical pathwise method to allow discontinuity in the payoffs. We show how to apply the new pathwise method to the first-and second-order Greeks and propose kernel estimators that require little analytical efforts and are very easy to implement. The numerical results show that our estimators work well for practical problems.