In this paper, we present a method for the accurate estimation of the derivative (aka. sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression.The method is an improvement of the approach presented in [Risk...

In this paper we consider the object oriented implementation of numerical algorithms where arithmetic operators (add, mult, exp) operate on objects with more complex structure (compared to floating point numbers). Examples are objects representing vectors instead of scalars, random variables,...

In this short note we derive an exact simulation scheme for the joint distribution of (r(t),N(t)), where r denotes the short rate following a Hull-White model and $N$ denotes the numeraire.To sample the correct joint distribution of (r(t),N(t)) our scheme requires a two-factor Brownian driver....

In this note we apply the stochastic (backward) automatic differentiation to calculate stochastic forward sensitivities. A forward sensitivity is a sensitivity at a future point in time, conditional to the future states (i.e., it is a random variable). A typical application of stochastic forward...

In this paper we re-formulate the automatic differentiation (and in particular, the backward automatic differentiation, also known as adjoint automatic differentiation, AAD) for random variables. While this is just a formal re-interpretation it allows to investigate the algorithms in the...

In this paper we present an efficient implementation of automatic differentiations of random variables (see 'https://ssrn.com/abstract=2995695' https://ssrn.com/abstract=2995695).Using this implementation can increase the speed of the calculation of the automatic differentiation and reduce the...

Funding costs are the costs to a (risky) institution of providing and managing its future cash flows in excess of, say, some risk free funding. For a single deterministic cash flow with maturity T these costs are essentially given by the ratio of the risky bond and the risk free bond. They can...

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...