On the sensitivity of greek kernel estimators to bandwidth parameters

The Greeks measure the rate of change of (financial) derivative prices with respect to underlying market parameters, which is essential in financial risk management. This paper focuses on a modified pathwise method that overcomes the difficulty of estimating Greeks with discontinuous payoffs as well as second-order Greeks and involves a kernel estimator whose accuracy/performance relies on a smoothing parameter (bandwidth). We explore the accuracy of the Greek delta, vega, and theta estimators of Asian digital options and up-and-out barrier call options with varying bandwidths. In addition, we investigate the sensitivity of a proposed iterative scheme that generates the “optimal” bandwidth. Our numerical experiments indicate that the Greek estimators are quite sensitive to the bandwidth choice, and the “optimal” bandwidth generated is sensitive to input parameters.