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...

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 short note we give the concept of “funding markets” and “fund exchange processes” and show that the valuation of derivative products, including different means of funding, is analog to the valuation of multi-currency derivatives. Hence, modeling of different fundings is analog to...

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...

In this short note we show how to setup a one dimensional single asset model, e.g. equity model, which calibrates to a full (two dimensional) implied volatility surface. We show that the efficient calibration procedure used in LIBOR Markov functional models may be applied here too. In a addition...

We consider a general Itocirc; stochastic process dX(t) = micro;(t,X(t)) dt + sigma(t,X(t)) dW(t)We show that the increment X(ti+1)-X(ti+1) of k Euler discretization steps of size h/k is equivalent to the increment X(ti+1)-X(ti+1) of one Euler step of step size h of an SDE with diffusion matrix...

In this article we give a short overview on sensitivity calculation using Monte-Carlo simulation and an introduction to the proxy simulation scheme method. We shortly discuss the localization technique and the implementation

In this paper we present a simple yet generic method for fast and robust Monte-Carlo calculation of sensitivities of Collateralized Debt Obligations (CDOs). The method is product independent and only relies on four pricings against modified models. From a modeling perspective the method is also...