Real-Time Risk Management: An AAD-PDE Approach

Abstract

We apply adjoint algorithmic differentiation (AAD) to the risk management of derivative securities in the situation where the dynamics of securities prices are given in terms of partial differential equations (PDE). With simple examples, we show how AAD can be applied to both forward and backward PDEs in a straightforward manner. In particular, in the context of one-factor short-rate models for interest rates or default intensity processes, we show how one can compute price sensitivities reliably and orders of magnitude faster than with a standard finite-difference approach. This significantly increased efficiency is obtained by combining (i) the adjoint of a forward PDE for calibrating the parameters of the model, (ii) the adjoint of a backward PDE for pricing the derivative security, and (iii) the implicit function theorem to avoid iterating the calibration procedure.