For the numerical calculation of partial derivatives (aka.~sensitivites or greeks) from a Monte-Carlo simulation there are essentially two possible approaches: The pathwise method and the likelihood ratio method. Both methods have their shortcomings: While the pathwise method works very well for...

We consider a generic framework which allows to calculate robust Monte-Carlo sensitivities seamlessly through simple finite difference approximation. The method proposed is a generalization and improvement of the proxy simulation scheme method (Fries and Kampen, 2005). As a benchmark we apply...

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...

This paper empirically investigates whether continuous time spot price models are able to help to reveal mispriced commodity futures contracts. Mispricings are identified based on the difference between model and observed prices, using four different models for four different markets, namely the...

In this paper we develop a multi-factor model for the joint dynamics of related commodity spot prices in continuous time. We contribute to the existing literature by simultaneously considering various commodity markets in a single consistent model and show in an application the economic...