1. Dynamic Conditional Correlation Models with Asymmetric Multivariate Laplace Innovations
Juan P. Cajigas
Centre for Econometric Analysis
Cass Business School, London

2. Dynamic Conditional Correlation (S,L) [Engle (2002), Engle and Sheppard (2001)]

3. Implications of the assumption of normality
Normality-MLE/QMLE = feasible + consistent but inefficient DCC coefficients (Bollerslev and Wooldridge, 1992)
Normality is not a satisfactory property for financial time series.
Non normal distribution to achieve efficiency with implication for the first stage
Importance of efficiency for
Portfolio allocation
VaR Analysis (Risk)

4. The main contribution of this paper: (AML)-ADDCC (1,1)
We propose an AGDCC (1,1) model and its nested versions using the Asymmetric Multivariate Laplace (AML) distribution for the vector of standardized residuals.
This is a special case of the Geometric Stable law (Kotz, Kozubowski and Podgorski, 2003)
It preserves convolution properties
It has finite variance,
It has a closed-form,
It allows for leptokurtosis and asymmetries.

5. The AML distribution (...continue)
Geometric Stable Distributions:

6. The AML distribution (...continue) NO
If we have that,
then

7. The AML distribution (...continue)
Main properties:
Tail behavior governed by the index of stability. For the AML distribution
Density function:
where v = (2 - n)/2 and Kv(u) is the modified Bessel function of the “third kind”

8. The AML distribution Mixtures of normal distributions representation:
where Y~N(0,H), Z~exp(1) and X~AML(m,H). Therefore,

9. AML distribution

10. Two-Step estimation: feasible (1…)
Normal case (Engle, 2002; Engle and Sheppard, 2001)

11. Two-Step estimation: feasible (…2)
Normal case
Engle (2002): uses Newey-McFadden (1994, HoE) results on GMM to justify the use of MLE for consistency

12. AML Two-Step estimation: feasible
FIRST STEP: Conditional variances

13. AML Two-Step estimation: feasible
SECOND STEP: Conditional correlations

14. AML Two-Step estimation: feasible
For n = 2s + 3, s = 0,1,… the Bessel function has a closed form that transforms the density function to:

15. AML Two-Step estimation: feasible
In this case we have:

16. Empirical applications (1): Modelling using DCC models
Data as in Cappiello, Engle and Sheppard (2004)
a) FTSE All-World weekly indices converted to US denominated returns for 21 countries and
b) Bond indices of 12 constructed by Datastream.
Sample Period: 08/01/ /02/2001

17. Main findings from the empirical application using stocks/bonds
Significant differences with Cappiello et al (2004) in the asymmetric models (AGDCC and ADCC):
Asymmetric terms much smaller when the AML distribution is used instead of the normal
Log-likelihood does not increase with the inclusion of asymmetries when the AML distribution is used

18. Main findings from the empirical application
Distribution of conditional correlations:
Much higher kurtosis when the AML distribution is used.
The impact of this feature “could” be relevant for VaR applications