Calculation of portfolio risk distributions, e.g. as used in the calculation of a "value at risk", may involve a huge number of valuations for every single financial product in a portfolio. The usual situation is that a distribution of market scenarios is given by a very large set (a sample) of...

Looking at the valuation of a swap when funding costs and counterparty risk are neglected (i.e. when there is a unique risk free discounting curve), it is natural to ask "What is the discounting curve of a swap in the presence of funding costs, counterparty risk and/or collateralization?".In...

In this note we discuss the definition, construction, interpolation and application of curves.We will discuss discount curves, a tool for the valuation of deterministic cash-flows and forward curves, a tool for the valuation of linear cash-flows of (possibly) stochastic indices.The aim of this...

By introducing a funding cost component like a funding valuation adjustment (FVA) into the valuation of derivatives, the replication strategy inherent in the valuation approach needs to be reflected in the real management of the position. Whilst in theory the replication takes place in one self...

In this note we derive a modified backward automatic differentiation (a.k.a. adjoint automatic differentiation, adjoint algorithmic differentiation) for algorithms containing conditional expectation operators and/or indicator functions. Bermudan option and xVA valuation are prototypical...

This first part of this presentation gives an introduction to stochastic automatic differentiation and its application.The second part of the presentation introduces a simple "static hedge" approximation for an SIMM based MVA and compares it with an exact solution (where the exact solution was...