Fairing the gamma: an engineering approach to sensitivity estimation

Abstract

In the finance industry, obtaining stable estimates for sensitivities of derivatives to price changes in an underlying asset is very important from a practical point of view. However, this aim is often hindered by the absence of closed-form expressions for Greeks or the requirement of an excessive computational workload due to the complexities of various exotic derivative structures. However, ad hoc numerical schemes to produce stable Greeks such as nonlinear regression can result in nonsensical values. This article proposes a fairing algorithm designed for the computation of gamma values of exotic derivatives. Examples are presented at exotic derivatives to which the algorithm is applied and some analytical and numerical results are provided that show its usefulness in reducing the mean square error of gamma estimates.