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 paper we consider the valuation of total return swaps (TRS). Since a total return swap is a collateralized derivative referencing the value process of an uncollateralized asset it is in general not possible that both counter parties agree on a unique value. Consequently it is not...

In this note we consider a classical term structure model framework, that is, a HJM framework on a time-discrete tenor, like the LIBOR market model, using a sequence of tenor discretization, where the tenors are valid for a specific simulation time interval.The setup then allows to model dynamic...

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...

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...

With the realization in the markets and the regulatory world that Interbank Offered Rates (IBORs) may not be as stable and robust as necessary to represent sustainable, global interest rate benchmarks, the search for alternatives has led to (secured or unsecured) overnight rates. The question of...

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,...

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...

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...