Validate Correlation of an ESG: Treasury Yields across
Within 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.
|Date of creation:||Jul 2011|
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- 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.
- 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.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
- 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.
- Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 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.
- Xin Jin & John M Maheu, 2009. "Modelling Realized Covariances," Working Papers tecipa-382, University of Toronto, Department of Economics.
- 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.
- Nakatani, Tomoaki & Teräsvirta, Timo, 2007. "Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model," SSE/EFI Working Paper Series in Economics and Finance 649, Stockholm School of Economics, revised 24 Jan 2007.
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