"Value-at-risk forecasts under scrutiny - the German experience" with Gerhard Stahl and Richard Stehle, Quantitative Finance, volume 7, issue 6, 2007-11-28.
We present an analysis of the VaR forecasts and the P&L series of all 12 German banks that used internal models for regulatory purposes throughout the period from the beginning of 2001 to the end of 2004.
"Internal models in Solvency II" with Gerhard Stahl, Life and Pensions, 2007-03-01.
The goals and principles of regulation of internal models in Solvency II are similar to the goals of regulation in the banking sector, but there are some unique differences. This paper looks at the challenges specific to the insurance sector.
"Consistent price systems for subfiltrations" with Andreas Gombani and Wolfgang Runggaldier, published online 2007-03-01, ESAIM Probability and Stochastics, volume 11, Aug 2007, pp. 35-39.
Asymmetric or partial information in financial markets may be represented by different filtrations. We consider the case of a larger filtration F – the natural filtration of the “model world” – and a subfiltration F-'hat' that represents the information available to an agent in the “real world”.
"VaR und gut" with Gerhard Stahl and Andreas Zapp, Risknews, volume 1, issue 5, pp.27-29, Sep 2004.
Experience with German banks' Value-at-Risk models from the supervisory perspective.
"A filtered no arbitrage model for term structures of noisy data" with Andrea Gombani and Wolfgang Runggaldier, Stochastic Processes and Their Applications, volume 115, issue 3, March 2005, pp. 381-400.
We consider an affine term structure model of interest rates, where the factors satisfy a linear diffusion equation. We assume that the information available to an agent comes from observing the yields of a finite number of traded bonds and that this information is not sufficient to reconstruct exactly the factors. We derive a method to obtain arbitrage-free prices of illiquid or non traded bonds that are compatible with the available incomplete information. The method is based on an application of the Kalman filter for linear Gaussian systems.
"A note on the inhomogeneous linear stochastic differential equation", 2003-07-21, Insurance: Mathematics and Economics, volume 32, issue 3, 2003, pp. 461-464.
The inhomogeneous linear SDE for general semimartingales is given in a form more general than the solution by Yoerp and Yor (1977).
"Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors" with Claudia Klüppelberg and Alexander Lindner, 2004-02-01, Journal of Multivariate Analysis, volume 88, issue 2, Feb 2004, pp. 252-273.
We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta-gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.
"Approximating Value at Risk in Conditional Gaussian Models" with Yuze Yiang, 2002, in Applied Quantitative Finance, Springer, edited by Wolfgang Härdle, Torsten Kleinow, and Gerhard Stahl.
VaR methods summarized and implemented in Xplore.
"The Cornish-Fisher-Expansion in the Context of Delta-Gamma-Normal Approximations", 2002, Journal of Risk, vol 4(4), pp.33-52.
Qualitative and quantitative properties of the Cornish–Fisher expansion in the context of Delta–Gamma-normal approaches to the computation of value-at-risk are presented. Some qualitative deficiencies of the Cornish-Fisher expansion – neither the monotonicity of the distribution function nor convergence are guaranteed – make it seem unattractive. In many practical situations, however, its actual accuracy is more than sufficient and the Cornish–Fisher approximation can be computed faster (and more simply) than other methods, such as numerical Fourier inversion. This paper attempts to provide a balanced view on when and when not to use the Cornish–Fisher expansion in this context.
"Error analysis of quantile-approximations using Fourier inversion in the context of delta-gamma-normal models" in the "Maths of all angles" section, GARP Risk Review, May/June 2002, vol.6, pp.28-33.
Provides a worst-case error analysis of FFT-based approximations to Fourier inversion in the context of delta-gamma-normal models for VaR.
"Coherent Risk Measures and Good-Deal Bounds" with Uwe Küchler, 2001, Finance and Stochastics, vol 5(2), p.181-200.
The relation between coherent risk measures, valuation bounds, and certain classes of portfolio optimization problems is established. One of the key results is that coherent risk measures are essentially equivalent to generalized arbitrage bounds, named “good deal bounds” by Cerny and Hodges (1999).
"Arbitrage und die Gültigkeit des Barwertprinzips im Markt für Bundeswertpapiere" with Richard Stehle and Stephan Wernicke. Zeitschrift für betriebswirtschaftliche Forschung, Jul/Aug 2000, pp.440-468.
Ausgangspunkt der Arbeit ist das Problem, die zeitliche Struktur der Zinssätze aus Preisen von Kuponanleihen zu bestimmen. Für den deutschen Rentenmarkt ist die bestmögliche Anpassung - völlig unabhängig vom verwendeten Regressionsverfahren - durch relative Bewertungsfehler von zeitweise über 3% gekennzeichnet. Im Mittelpunkt der Arbeit steht die Frage, warum die Preisdiskrepanzen so groß sind.
"Arbitrage Bounds for the Term Structure of Interest Rates", 1998, Finance and Stochastics, vol 2(1), pp.29-40.
This paper proposes a methodology for simultaneously computing a smooth estimator of the term structure of interest rates and economically justified bounds for it.
"Super-Hedging and Arbitrage Pricing of Bonds and Interest Rate Derivatives", Dissertation 1998, Shaker-Verlag, Aachen, ISBN 3-8265-3380-1.
"Quantile-VaR is the Wrong Measure to Quantify Market Risk for Regulatory Purposes" (2001), Discussion Paper 2001-55, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin.
"The Cornish-Fisher-Expansion in the Context of Delta-Gamma-Normal Approximations" (2001), Discussion Paper 2001-54, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin.
"Coherent Risk Measures, Valuation Bounds, and (mu,rho)-Portfolio Optimization" (1999), Discussion Paper 99-64, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin.
"Higher Order Forward Rate Agreements and the Smoothness of the Term Structure" (1999), Discussion Paper 99-13, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin.
"A note on Stochastic Volatility, GARCH models, and Hyperbolic Distributions" (1997), originally published as Discussion Paper 98-23, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin. An updated version was published 2000.
"Super-Hedging and Arbitrage Pricing in Markets with Transaction Costs and Trading Constraints". This is a revised version of a part of my dissertation, completed Dec 2006 during my PostDoc time at Laboratoire de Probabilités (at Jussieu Paris).
"A note on the Present Value Principle in Markets with Transaction Costs" (1996), Discussion Paper 96-57, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin.
"Arbitrage Bounds for the Term Structure of Interest Rates" (1995), Discussion Paper 95-35, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin.
"Exploratory Data Analysis of Short-Term Interest Rates" (1994), Discussion Paper 94-47, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin.