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We consider "copula skew models" that account for the correlation smile in the pricing of synthetic CDO tranches. These can be viewed as stochastic or local correlation models and are extensions of the well-known one factor Gaussian copula model. We analyse these models through their conditional default probability distributions and marginal compound correlations. We also give some examples of using a particular stochastic correlation model to fit the market, illustrating the stability of the parameters over time.
11831 Downloads07.12.2006
Datei downloaden Multivariate GARCH (MGARCH) models are usually estimated under multivariate normality. In this paper, for non-elliptically distributed financial returns, we propose copulabased multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our new C-MGARCH model nests a conventional MGARCH model as a special case. We apply this idea to the three MGARCH models, namely, the dynamic conditional correlation (DCC) model of Engle (2002), the varying correlation (VC) model of Tse and Tsui (2002), and the BEKK model of Engle and Kroner (1995). Monte Carlo experiment is conducted to illustrate the performance of C-MGARCH vs MGARCH models. Empirical analysis with a pair of the U.S. equity indices and two pairs of the foreign exchange rates indicates that the C-MGARCH models outperform DCC, VC, and BEKK in terms of in-sample model selection criteria (likelihood, AIC, SIC) and out-of-sample multivariate density forecast.
7778 Downloads07.12.2006
Datei downloaden Lévy copulas are functions that completely characterize the law of a multidimensional Lévy process given the laws of its components. In this paper, after recalling the basic properties of Levy copulas, we discuss the simulation of multidimensional Lévy processes with dependence structure given by a Lévy copula. Being able to describe the dependence structure of a Lévy process in terms of its Lévy copula allows us to quantify the effect of dependence on the prices of basket options in a multidimensional exponential Lévy model. We conclude that these prices are highly sensitive not only to the linear correlation between assets but also to the exact type of dependence beyond linear correlation.
8584 Downloads07.12.2006
Datei downloaden In this article we focus on the latent variable approach to modelling credit portfolio losses. This methodology underlies all models that descend from Merton's firm-value model (Merton 1974). In particular, it underlies the most important industry models, such as the model proposed by the KMV corporation and CreditMetrics. In these models default of an obligor occurs if a latent variable, often interpreted as the value of the obligor's assets, falls below some threshold, often interpreted as the value of the obligor's liabilities. Dependence between default events is caused by dependence between the latent variables. The correlation matrix of the latent variables is often calibrated by developing factor models that relate changes in asset value to changes in a small number of economic factors. [Rüdiger Frey, Swiss Banking Institute, University of Zurich / Alexander J. McNeil, Department of Mathematics, ETH Zurich / Mark A. Nyfeler, Investment Office RTC, UBS Zurich]
9748 Downloads07.12.2006
Datei downloaden The t copula and its properties are described with a focus on issues related to the dependence of extreme values. The Gaussian mixture representation of a multivariate t distribution is used as a starting point to construct two new copulas, the skewed t copula and the grouped t copula, which allow more heterogeneity in the modelling of dependent observations. Extreme value considerations are used to derive two further new copulas: the t extreme value copula is the limiting copula of componentwise maxima of t distributed random vectors; the t lower tail copula is the limiting copula of bivariate observations from a t distribution that are conditioned to lie below some joint threshold that is progressively lowered. Both these copulas may be approximated for practical purposes by simpler, better-known copulas, these being the Gumbel and Clayton copulas respectively. [Stefano Demarta & Alexander J. McNeil, Department of Mathematics, Federal Institute of Technology, ETH]
10085 Downloads07.12.2006
Datei downloaden We propose a new method to compute option prices based on GARCH models. In an incomplete market framework, we allow for the volatility of asset return to differ from the volatility of the pricing process and obtain adequate pricing results. We investigate the pricing performance of this approach over short and long time horizons by calibrating theoretical option prices under the Asymmetric GARCH model on S&P 500 market option prices. A new simplified scheme for delta hedging is proposed. [Author: Giovanni Barone-Adesi (University of Lugano), Robert Engle (New York University - Department of Economics; National Bureau of Economic Research), Loriano Mancini (University of Zurich - Swiss Banking Institute)]
7489 Downloads28.11.2006
Datei downloaden It is a well-documented empirical fact that index option prices systematically differ from Black-Scholes prices. However, previous research provides inconclusive results whether the observed volatility smile could be explained by a discrete-time dynamic model of stock returns with skewed, leptokurtic innovations. The improvements in pricing errors are particularly pronounced for out-of-the money put options, while the models partly underperform a Gaussian alternative for near-the-money options. Motivated by theses empirical evidence, I develop a new GARCH option-pricing model with a more flexible innovation structure. In an application of the model to DAX index options, I test the relative performance of the approach against a standard nested GARCH specification and the wellknown practitioners Black-Scholes model. I show that the performance of the truncated Lévy GARCH option pricing model is superior to existing approaches. [Author: Thorsten Lehnert, Limburg Institute of Financial Economics (LIFE), Maastricht University]
10159 Downloads28.11.2006
Datei downloaden Die volkswirtschaftliche Aufgabe einer Bank ist es, als Kapital- und Kreditvermittlerin einen Marktplatz für unterschiedliche Volumina und Laufzeiten von Finanztransaktionen bereitzustellen sowie die Risikotransformation zu übernehmen. Bei Zinsänderungsrisiken sind in erster Linie die unterschiedlichen Laufzeiten (Fristigkeiten) von Interesse. Ist eine Bank vorwiegend kurzfristig refinanziert und transformiert diese Gelder in langfristige Anlagen, profitiert sie vom üblicherweise vorhandenen Termspread zwischen kurz- und langfristigen Zinsen. Sie geht dabei aber gleichzeitig das Risiko ein, dass im Falle einer Erhöhung des Zinsniveaus die Einlagen schneller an das neue Niveau angepasst werden müssen als die Ausleihungen. [Quelle: RISIKO MANAGER 22/2006]
12465 Downloads04.11.2006
Datei downloaden Schätzungen von Verlustquoten (loss given default, LGD) sind in der Bankenlandschaft nach wie vor deutlich weniger entwickelt als etwa Verfahren zur Schätzung von Ausfallwahrscheinlichkeiten (probability of default, PD). In der Modelllandschaft des Risikomanagements von Banken nehmen LGD-Modelle eine untergeordnete Rolle ein. Bis vor einigen Jahren noch gänzlich fehlend, steuern viele Banken ihr Geschäft heute mit einer pro Segment konstant erwarteten Verlustquote, die auf der Basis historischer Ausfalldaten geschätzt wird. [Quelle: RISIKO MANAGER 20/2006]
5242 Downloads04.11.2006
Datei downloaden Das Hedge Management im Bankenbuch wurde bisher im Wesentlichen nach ökonomischen Gesichtspunkten durchgeführt. Im Rahmen des Aktiv-/Passivvmanagements (ALM) wurden die „Überhänge“ ermittelt, Sicherungsstrategien erarbeitet und entsprechende Geschäfte abgeschlossen.
10196 Downloads04.11.2006
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