Adjoint Greeks Made Easy

Luca Capriotti and Michael Giles

The renewed emphasis of the financial industry on quantitatively sound risk management practices comes with formidable computational challenges. Computationally intensive Monte Carlo simulations are often the only practical tool available, and standard approaches for the calculation of risk require repeated simulation of a portfolio’s profit and loss.

Several faster alternative methods for the calculation of price sensitivities have been proposed in the literature (for a review see, for example, Glasserman 2004). Among these, the pathwise derivative method (Broadie and Glasserman 1996) provides unbiased estimates at a computational cost that may be smaller than standard finite-differences approaches. A very efficient implementation of the pathwise derivative method was proposed in Giles and Glasserman (2006) in the context of the London Interbank Offered Rate (Libor) market model (LMM) for European payouts. This was later generalised to Bermudan options by Leclerc et al (2009) and extended by Denson and Joshi (2011). The latter express the calculation of the pathwise derivative estimator in terms of linear algebra operations, and use adjoint methods to reduce the overall