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...

We consider a generic framework for generating likelihood ratio weighted Monte Carlo simulation paths, where we use one simulation scheme K° (proxy scheme) to generate realizations and then reinterpret them as realizations of another scheme K* (target scheme) by adjusting measure (via...

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...

We consider a generic framework for generating likelihood ratio weighted Monte Carlo simulation paths, where we use one simulation scheme (proxy scheme) to generate realizations and then reinterpret them as realizations of another scheme (target scheme) by adjusting measure (via likelihood...

In this paper we investigate the so called foresight bias that may appear in the Monte-Carlo pricing of Bermudan and compound options if the exercise criteria is calculated by the same Monte-Carlo simulation as the exercise values. The standard approach to remove the foresight bias is to use two...

In this paper we present a generic method for the Monte-Carlo pricing of (generalized) auto-callable products (aka. trigger products), i.e., products for which the payout function features a discontinuity with a (possibly) stochastic location (the trigger) and value (the payout).The Monte-Carlo...

In this paper we discuss the valuation and sensitivities of financial products with early exercise rights (e.g., Bermudan options) using a Monte-Carlo simulation. The usual way to value early exercise rights is the backward algorithm. As we will point out, the Monte-Carlo version of the backward...