Kernel Estimation of the Greeks for Options with Discontinuous Payoffs

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.