We show how algorithmic differentiation can be used as a design paradigm to implement the adjoint calculation of sensitivities in Monte Carlo in full generality and with minimal analytical effort. With several examples we illustrate the workings of this technique and demonstrate how it can be...

Adjoint algorithmic differentiation can be used to implement efficiently the calculation of counterparty credit risk. We demonstrate how this powerful technique can be used to reduce the computational cost by hundreds of times, thus opening the way to real time risk management in Monte Carlo

Adjoint Algorithmic Differentiation is one of the principal innovations in risk management of the recent times. In this paper we show how this technique can be used to compute real time risk for credit products

We investigate the use of Antithetic Variables, Control Variates and Importance Sampling to reduce the statistical errors of option sensitivities calculated with the Likelihood Ratio Method in Monte Carlo. We show how Antithetic Variables solve the well-known problem of the divergence of the...

We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least squares optimization procedure. With several numerical examples, we show that such Least Squares Importance Sampling (LSIS) provides efficiency gains comparable to the state of the art techniques, when...

In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a series expansion of the deviation of its logarithm from...

A recently introduced Importance Sampling strategy based on a least squares optimization is applied to the Monte Carlo simulation of Libor Market Models. Such Least Squares Importance Sampling (LSIS) allows the automatic optimization of the sampling distribution within a trial class by means of...