Ch.3 Multivariate Models Flashcards
Say we denote the number of assets by K, what the total number of terms to estimate in the covariance matrix?
K + K(K-1)/2
What assumption must be imposed in multivariate models that isn’t necessary in univariate ones?
Stationarity assumption.
What are two common numerical issues encountered in MV models?
Flat surfaces and multiple local minima.
What are the pros and cons of the multivariate EWMA?
- Straightforward even for large K.
- Guaranteed pos.def cov. matrix
- Too simple
- Assumption of single non-estimated lambda.
Describe the 3 steps behind CCC and DCC
- Estimate volatility, i.e. variance, of each asset using a univariate model.
- recover residuals.
- Use return residuals to retrieve Covariance Matrix.
Given a CCC model, how would one retrieve the residuals?
Divide the returns by their respective conditional variance.
What are the Pros and Cons of Constant Conditional Correlation models?
What is the main issue faced by Dynamic Conditional Correlations modelling of correlations?
The matrix is not always positive definite.
Explain the trick used in DCC to ensure a positive definite covariance matrix.
In a DCC model, how does one model the Q_t matrix of the Correlation matrix?
Let Q_t follow a GARCH process with constant parameters.
What are the Pros and Cons of CCC models?
Say you are a large bank with thousands of assets. What is one way to reduce the modelling problem into a easier one?
Group assets together by category and model correlations as constant between groups.
