Greeks with continuous adjoints: fast to code, fast to run

The continuous adjoint method for computing risk figures of options that can be priced with partial differential equations is elegant, flexible and robust. It can be implemented in legacy codes with minimal code modifications and in particular without using tools such as automatic differentiation. Numerical results on the production environment for foreign exchange options using a local stochastic volatility model show important speed improvements. The authors report their experience of analysing and implementing this technique

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Adjoint methods are a hot topic in computational finance. They have a long history outside the financial industry and have been used extensively in optimal control theory, shape optimisation and especially in fluid dynamics (Jameson 1988), design optimisation and many other fields (see Newman et al (1999) and Giles & Pierce (2000) for an overview). The seminal article of Giles & Glasserman (2006) has shown their potential for financial applications using