Skip to main content
Article thumbnail
Location of Repository

Co-volatility and correlation clustering : a multivariate correlated ARCH framework

By George Christodoulakis

Abstract

We present a new, full multivariate framework for modelling the evolution of conditional correlation between financial asset returns. Our approach assumes that a vector of asset returns is shocked by a vector innovation process the covariance matrix of which is timedependent. We then employ an appropriate Cholesky decomposition of the asset covariance matrix which, when transformed using a Spherical decomposition allows for the modelling of conditional variances and correlations. The resulting asset covariance matrix is guaranteed to be positive definite at each point in time. We follow Christodoulakis and Satchell (2001) in designing conditionally autoregressive stochastic processes for the correlation coefficients and present analytical results for their distribution properties. Our approach allows for explicit out-of-sample forecasting of conditional correlations and generates a number of observed stylised facts such as time-varying correlations, persistence and correlation clustering, co-movement between correlation coefficients, correlation and volatility as well as between volatility processes (co-volatility). We also study analytically the co-movement between the elements of the asset covariance matrix which are shown to depend on their persistence parameters. We provide empirical evidence on a trivariate model using monthly data from Dow Jones Industrial, Nasdaq Composite and the 3-month US Treasury Bill yield which supports our theoretical arguments

Topics: HF, QA
Publisher: Warwick Business School Financial Econometrics Research Centre
Year: 2001
OAI identifier: oai:wrap.warwick.ac.uk:1822

Suggested articles

Citations

  1. A New Measure of Herding and Empirical Evidence, doi
  2. A Panel-Based Investigation into the Relationship Between Stock Prices and Dividends,
  3. An Analysis of Performance Measures Using Copulae, doi
  4. An Analysis of the Performance of European Foreign Exchange Forecasters, doi
  5. An Elementary Account of Amari's Expected Geometry, doi
  6. An Introduction to Differential Geometry in Econometrics, doi
  7. Ana-Maria Fuertes and Maria-Teresa Perez, Numerical Issues in Threshold Autoregressive Modelling of Time Series, doi
  8. Calculating the Miss-specification in Beta from Using a Proxy for the Market Portfolio, doi
  9. Co-Volatility and Correlation Clustering: A Multivariate Correlated ARCH Framework,
  10. Currency Spillovers and Tri-Polarity: a Simultaneous Model doi
  11. Evaluating the Performance of Nearest Neighbour Algorithms when Forecasting US Industry Returns,
  12. Evolving Systems of Financial Returns: AutoRegressive Conditional Beta,
  13. Finite Sample Inference for Extreme Value Distributions,
  14. Forecasting Inflation with a Non-linear Output Gap Model,
  15. Forecasting T-Bill Yields: Accuracy versus Profitability,
  16. From Market Micro-structure to Macro Fundamentals: is there Predictability in the Dollar-Deutsche Mark Exchange Rate?,
  17. Hopscotch Methods for Two State Financial Models, doi
  18. How do UK-Based Foreign Exchange Dealers Think Their Market Operates?, WP99-21 2. Soosung Hwang, doi
  19. Implied Volatility Forecasting: A Compaison of Different Procedures Including Fractionally Integrated Models with Applications to UK Equity Options,
  20. Improved Testing for the Efficiency of Asset Pricing Theories in Linear Factor Models,
  21. Investigating Dynamic Dependence Using Copulae, doi
  22. Market Risk and the Concept of Fundamental Volatility: Measuring Volatility Across Asset and Derivative Markets and Testing for the Impact of Derivatives Markets on Financial Markets, doi
  23. Modelling Emerging Market Risk Premia Using Higher Moments, doi
  24. Multivariate Extremes at Work for Portfolio Risk Measurement,
  25. On the Evolution of Credibility and Flexible Exchange Rate Target Zones,
  26. Option Hedging with Stochastic Volatility, doi
  27. Properties of Cross-sectional Volatility, doi
  28. Rationality Testing under Asymmetric Loss, doi
  29. Rethinking the Forward Premium Puzzle in a Nonlinear Framework,
  30. Robust Decision Theory and the Lucas Critique, doi
  31. Soosung Hwang and Stephen Satchell, Using Bayesian Variable Selection Methods to Choose Style Factors in Global Stock Return Models, doi
  32. Technical Analysis and Central Bank Intervention, doi
  33. The Asset Allocation Decision in a Loss Aversion World, doi
  34. The Derivation of New Model of Equity Duration,
  35. The Effects of Systematic Sampling and Temporal Aggregation on Discrete Time Long Memory Processes and their Finite Sample Properties, doi
  36. The Felsdtein-Horioka Puzzle is Not as Bad as You Think, doi
  37. Tracking Error: Ex-Ante versus Ex-Post Measures, doi
  38. Vado Durrleman, Ashkan Nikeghbali, Gael Riboulet and Thierry Roncalli, Copulas: an Open Field for Risk Management, doi
  39. Valuing Information Using Utility Functions, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.