Nonlinear term structure dependence: Copula functions, empirics, and risk implications

Junker, Markus; Szimayer, Alex; Wagner, Niklas

doi:10.1016/j.jbankfin.2005.05.014

Cited by 61 publications

(19 citation statements)

References 42 publications

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“…They are uniform distributions that enable to extract the dependence structure from the joint probability distribution function of a set of random variables and, at the same time, to separate the dependence structure from the univariate marginal behavior. Few examples of recent applications of copulas in finance are given in Cherubini and Luciano (2002, 2003a, 2003b, Embrechts, Lindskog, and McNeil (2003), Giesecke (2004), Junker, Szimayer, and Wagner (2006), Pachenko (2005), and Rosenberg and Schuermann (2006). A thorough discussion on the use of copulas in finance is provided in the textbook by Cherubini, Luciano, and Vecchiato (2004).…”

Section: Copulasmentioning

confidence: 99%

Multi‐period hedge ratios for a multi‐asset portfolio when accounting for returns co‐movement

Fernández

2007

Journal of Futures Markets

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This study presents a model to select the optimal hedge ratios of a portfolio composed of an arbitrary number of commodities. In particular, returns dependency and heterogeneous investment horizons are accounted for by copulas and wavelets, respectively. A portfolio of London Metal Exchange metals is analyzed for the period July 1993-December 2005, and it is concluded that neglecting cross correlations leads to biased estimates of the optimal hedge ratios and the degree of hedge effectiveness. Furthermore, when compared with a multivariate-GARCH specification, our methodology yields higher hedge effectiveness for the raw returns and their short-term components. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:182-207, 2008 Financial support from SOC 06/01-2 Grant (Research Division of the University of Chile) and from an institutional grant of the Hewlett Foundation to CEA is greatly acknowledged. All remaining errors are the author's. INTRODUCTIONThe determination of the optimal hedge ratio is an issue of both practical and theoretical interests as it impacts hedging effectiveness. Recent contributions to the literature on heterogeneous investors and the selection of an optimal hedge ratio have focused on a single commodity in isolation (e.g., In & Kim, 2006a, 2006bLien & Shrestha, 2007). This study presents a generalization of such an approach, in which the selection of optimal hedge ratios is considered for a portfolio composed of several net positions in commodities (i.e., cash position minus a proportion of a futures contract). In particular, an analytical expression is obtained for an optimal vector of hedge ratios and a measure of the degree hedge effectiveness (HE) for such a portfolio. Toward that end, wavelet and copula analysis is used to accommodate for the existence of heterogeneous investors and asset returns dependency, respectively. The empirical application used in this study considers a portfolio composed of cash and futures positions on London Metal Exchange (LME) metals for the sample period July 1993-December 2005. The portfolio choice is based on the grounds of data availability on cash and futures prices at a high frequency. Indeed, wavelet analysis is a computationally intensive statistical tool, which requires long time series (e.g., Gençay, Whitcher, & Selçuk, 2002;Percival & Walden, 2000). In contrast, given that the LME data have been analyzed earlier (e.g., McMillan, 2005), our conclusions can be contrasted with those of previous studies.The simulations we carry out to characterize the distribution functions of the hedge ratios and the degree of HE are performed under two scenarios: with and without accounting for the cross correlations of returns on cash and futures contracts. As mentioned above, dependency is handled by copula analysis, a statistical tool that has recently gained ground in the finance field to extract the dependence structure from the joint probability distribution function of a set of random variables (e.g., Cherubini, Luciano, & Vecchiato, 2004).Indeed, earlier at...

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Section: Copulasmentioning

confidence: 99%

Multi‐period hedge ratios for a multi‐asset portfolio when accounting for returns co‐movement

Fernández

2007

Journal of Futures Markets

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“…While the impact of copulas has been studied in relation to option pricing (see e.g. Frey and McNeil, 2003;Mashal et al, 2003;Hamerle and Rösch, 2005), the term structure of interest rates (see Junker et al, 2006) and credit risk (see Giesecke, 2004;Meneguzzo and Vecchiato, 2004), knowledge on the consequences of copulas for portfolios of linear assets is limited. Poon et al (2004) address this issue, but only consider Gaussian and Gumbel copulas.…”

Section: Introductionmentioning

confidence: 99%

Selecting copulas for risk management

Kole

Koedijk

Verbeek

2007

Journal of Banking & Finance

255

120

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Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student's t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student's t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.

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“…Junkera, Szimayerb, and Wagnerc (2006) provide evidence of the dependence structure within the term structure of the interest rates paid by U.S. Treasury instruments. Our approach is similar to theirs, however, while we focus on factors and macroeconomic variables, Junkera et al (2006) focused on the dependence relationship between short-term and long-term interest rates as represented by the two yield factors.…”

Section: Introductionmentioning

confidence: 96%

Joint dynamics of Brazilian interest rate yields and macro variables under a no-arbitrage restriction

Barbedo

Melo

2012

Journal of Economics and Business

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Nonlinear term structure dependence: Copula functions, empirics, and risk implications

Cited by 61 publications

References 42 publications

Multi‐period hedge ratios for a multi‐asset portfolio when accounting for returns co‐movement

Multi‐period hedge ratios for a multi‐asset portfolio when accounting for returns co‐movement

Selecting copulas for risk management

Joint dynamics of Brazilian interest rate yields and macro variables under a no-arbitrage restriction

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