Validate Correlation of an ESG: Treasury Yields across
AbstractWithin an internal model the Economic Scenario Generator (ESG) is an important component. In order to get a regulatory approval of an internal model it is required that the implemented models (must be) passed a rigorous validation process, see Ceiops . In this paper we focus on the particular problem to judge the contribution of correlations between interest rate risks across countries in the ESG. To that end we apply two strategies: an analytical and a statistical one. The analytical approach yields necessary conditions in terms of upper and lower bounds for correlations within the chosen model. A system of stochastic differential equations is used to describe several economies simultaneously. In this framework we derive a lower and upper bound of the correlation of the treasury yields between two economies by solving the associated ordinary differential inequalities. In order to deepen our understanding about the correlation structure we consider three modeling types of correlations of historical datasets. We first derive the realized correlations as outlined by Andersen et al.  for the historical treasury yields of two economies. Furthermore we include Engle’s parsimonious multivariate GARCH models – known as Dynamical Conditional Correlation (DCC) model, see Engle  – and we derive conditional correlations out of our ESG. We then exploit a nice relationship outlined by Andersen et al. , which relates the realized correlation and conditional correlations in oder to compare the three model by their ability to capture the stylized facts of the underlying processes. In this respect the long memory of the correlation processes is of particular importance. We give a series of statistical analysis that highlight the adequacy of the model.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät in its series Hannover Economic Papers (HEP) with number dp-476.
Length: 21 pages
Date of creation: Jul 2011
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-07-27 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002.
"Modeling and Forecasting Realized Volatility,"
02-12, Duke University, Department of Economics.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Nakatani, Tomoaki & Teräsvirta, Timo, 2007.
"Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model,"
Working Paper Series in Economics and Finance
649, Stockholm School of Economics, revised 24 Jan 2007.
- Tomoaki Nakatani & Timo Terasvirta, 2009. "Testing for volatility interactions in the Constant Conditional Correlation GARCH model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 147-163, 03.
- Xin Jin & John M Maheu, 2009. "Modelling Realized Covariances," Working Papers tecipa-382, University of Toronto, Department of Economics.
- Engle, Robert F & Sheppard, Kevin K, 2001.
"Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH,"
University of California at San Diego, Economics Working Paper Series
qt5s2218dp, Department of Economics, UC San Diego.
- Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Heidrich, Christian).
If references are entirely missing, you can add them using this form.