Stefan Ebenfeld
Grundlagen der Finanzmathematik
Mathematische Methoden, Modellierung von Finanzmärkten und Finanzprodukten
Schäffer-Poeschel Verlag, Stuttgart 2007

Jörn Rank (ed.)
Copulas - From theory to application in finance,
Risk Books, London 2006

Jörgen Topper
Financial Engineering with Finite Elements,
John Wiley and Sons Ltd, Chichester 2005

Hans-Peter Deutsch
Derivatives and Internal Models, 3rd edition,
Palgrave/MacMillan Verlag, London 2004
Book Review (ca. 300 KB) in Risk Magazine

Jörn Rank und Thomas Siegl
Application of Copulas for the Calculation of Value-at-Risk,
in W. Härtle, T. Kleinow und G. Stahl (Hrsg.): Applied Quantitative Finance,
Springer Verlag, Berlin - Heidelberg 2002
Abstract: We  focus on the computation of the Value-at-Risk (VaR) from the perspective of the dependency structure between the risk factors. Apart from historical simulation, most VaR methods assume some kind of multinormal distribution of the risk factors. Therefore, the dependence structure between different risk factors is defined by the correlation between these factors. It is shown in Embrechts et al. (1999) that the concept of correlation entails several pitfalls. The authors therefore propose the use of copulas to quantify dependence. For a good overview of copula techniques we refer to Nelsen (1999). Copulas can be used to describe the dependence between two or more random variables with arbitrary marginal distributions. In rough terms, a copula is a function C: [0,1]^n -> [0,1] with certain special properties. The joint multidimensional cumulative distribution can be written as Prob(X_1 <= x_1 , ..., X_n <= x_n) =   C(Prob(X_1 <= x_1), ..., Prob(X_n <= x_n)) = C(F_1(x_1), ..., F_n(x_n)), where F_1, ..., F_n denote the cumulative distribution functions of the n random variables X_1, ..., X_n. In general, a copula C depends on one or more copula parameters p_1, ..., p_k that determine the dependence between the random variables X_1, ..., X_n. In this sense, the correlation rho(X_i,X_j) can be seen as a parameter of the so-called Gaussian copula. Here we demonstrate the process of deriving the VaR of a portfolio using the copula method with XploRe, beginning with the estimation of the selection of the copula itself, estimation of the copula parameters and the computation of the VaR. Backtesting of the results is performed to show the validity and relative quality of the results. We will focus on the case of a portfolio containing two market risk factors only, the FX rates USD/EUR and GBP/EUR. Copulas in more dimensions exist, but the selection of suitable n-dimensional copulas is still quite limited. While the case of two risk factors is still important for applications, e.g. spread trading, it is also the case that can be best described. As we want to concentrate our attention on the modelling of the dependency structure, rather than on the modelling of the marginal distributions, we restricted our analysis to normal marginal densities. On the basis of our backtesting results, we find that the copula method produces more accurate results than "correlation dependence".

Tobias Herwig
Market-Conform Valuation of Options,
in Lecture Notes in Economics and Mathematical Systems, Vol. 571,
Springer-Verlag, Berlin - Heidelberg 2006
Abstract: We focus on the development of new approaches for the market-conform valuation of newly issued derivatives. The first chapter presents a flexible approach to construct the binomial process of the underlying asset price by using a simultaneously backward and forward induction algorithm. This framework can be used to price and hedge a wide range of plain-vanilla and exotic options. In the second chapter this new approach is compared to existing models using a sample of plain-vanilla options, American call options and European Barrier options from two competing markets. In the third chapter new methods to value American-style options via Monte Carlo simulations in accordance with given market prices are discussed. After a short introduction to Monte Carlo methods, two new approaches are proposed. These new frameworks are illustrated via pricing examples for standard American put options.

Hans-Peter Deutsch
Quantitative Portfoliosteuerung - Konzepte, Methoden, Beispielrechnungen,
Schäffer-Poeschel Verlag, Stuttgart 2005

V. Gehrmann, Gernot Blum, Christoph Bennemann
Risikomanagement von Verbriefungen und Kreditderivaten
in Gruber/Gruber/Braun, Praktiker-Handbuch Asset-Backed-Securities und Kreditderivate,
Schäffer-Poeschel Verlag, Stuttgart 2005

Oliver Schwarzhaupt, Christoph Bennemann
Emittentenrisiken im Kontext der MaK - Modellierungsansätze, Limitierung und Praxisrelevanz
in Becker/Gruber/Wohler, Handbuch Bankenaufsichtliche Entwicklungen,
Schäffer-Poeschel Verlag, Stuttgart 2004 

Mark Beinker und Hans-Peter Deutsch
Die drei Hauptmethoden zur VaR - Berechnung im Praxisvergleich,
in: Handbuch Bankenaufsicht und Interne Risikosteuerungsmodelle,
Schäffer-Poeschel-Verlag, Stuttgart 1999

Christoph Burmester, Christian Tobias Hille und Hans-Peter Deutsch
Risikoadjustierte Kapitalallokation: Beurteilung von Allokationsstrategien über einen Optimierungsansatz, in: Handbuch Bankenaufsicht und Interne Risikosteuerungsmodelle,
Schäffer-Poeschel-Verlag, Stuttgart 1999

Michael Röhl
GARCH-Modelle im Risikomanagement,
in: Handbuch Bankenaufsicht und Interne Risikosteuerungsmodelle,
Schäffer-Poeschel-Verlag, Stuttgart 1999

Thomas Siegl, Ansgar West, Markus von Rothkirch und Hans-Peter Deutsch
Erweiterung der Delta-Normal VaR-Methode um nichtlineare Risiken - der Dynamic-Hedge,
in: Handbuch Bankenaufsicht und Interne Risikosteuerungsmodelle,
Schäffer-Poeschel-Verlag, Stuttgart 1999

Hans-Peter Deutsch
Monte Carlo Simulationen in der Finanzwelt,
in: Handbuch des Risikomanagements,
Schäffer-Poeschel-Verlag, Stuttgart 1997