Adjoint Greeks made easy

Luca Capriotti and Michael Giles show how algorithmic differentiation can be used to systematically implement the adjoint calculation of sensitivities in Monte Carlo for general path-dependent and multi-asset options, with minimal analytical effort. With several examples, they illustrate the workings of this technique and demonstrate how it can be straightforwardly implemented to reduce the time required for the computation of the risk of any portfolio by orders of magnitude

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.

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