Generic Computing Alternatives for Better Greeks

Abstract

It is quite common in option pricing and risk management for Greeks to be computed through finite differences approximation (“bump-and-reprice”), due to simplicity, general applicability and acceptable accuracy (if bumping stepsize is properly selected). However this approach is time consuming and may not be very accurate. We present two generic alternative approaches with much better accuracy (up to machine precision) combined with a smaller computational footprint (sometimes by several orders of magnitude): complex-step derivative approximation (CSDA) and, respectively, adjoint automatic differentiation (AAD). While both procedures require additional development effort (rather minimal for CSAD and more challenging for AAD), both implementations are quite straightforward. We present numerical results, details of the implementations and we comment on which alternative approach should be preferred, given requirements and characteristics of the problem.