Description

Actions de Recherches Concertées 2007 - 2012:    "Econometric modelling of multivariate financial time series"

 

Multivariate time series modelling is of paramount importance in finance. Financial systems are complex, dynamic and interdependent. Although univariate models are useful, there is a lot to gain by using multivariate models for improving our scientific knowledge of such systems and our capacity to predict and manage their evolution. This is obvious since by nature financial systems link together many variables like asset prices and interest rates, not only in a given country, but all over the world. The volatility of asset prices is of great importance for the financial sector and for the whole economy as is regularly demonstrated by the negative economic and social consequences of financial crises in some regions of the world. Financial volatility, in a multivariate perspective, is a key concept in various areas of finance and financial management, such as asset pricing, portfolio selection, option pricing, hedging, and risk management in financial and related markets (like energy markets). For example, the construction of optimal portfolio allocation models, based on expected utility maximization subject to a budget constraint, requires to know the volatilities of different assets, but also the correlations between these (or more generally, their dependence structure). In derivative markets, there exist basket options that are defined in terms of several underlying assets. Pricing such options requires also to know the multivariate structure. Risk management is much more efficient and reliable if it takes account of the interdependence of risks than if it neglects this aspect.

 

Our research project aims to develop the scientific knowledge in the multivariate econo-metric modelling of financial systems. The research area known as “financial econometrics" has progressively emerged during the last ten to twenty years in economics and finance.

This has been recognized as a significant progress, witness in particular the attribution of a Nobel prize in economics to Robert Engle in 2003 for contributions in this field (see Engle 2004). This development is fundamentally related to that of financial markets, itself due to the economic growth that translates itself in increased wealth accumulation in the form of financial assets. Another important element behind the emergence of financial econometrics is the increased availability, at decreasing costs, of huge masses of financial data, due to technical progress in electronic storage.

 

More specifically, with our project we want to cope with two broad, related, challenges that arise in the multivariate modelling of financial time series:

 

We shall address these issues by two complementary approaches: non-linear models and latent factor models. To meet the challenge of complexity, we shall resort to models that are non-linear in their dependence structure on past information. These non-linearities correspond to asymmetries in macroeconomic cycles (economic recessions are shorter but often more acute than economic expansions), structural breaks, and regime switching. For example in financial series, it is known that volatilities react more nervously to bad news than to good news, and that periods of financial crises correspond to regime changes. We plan to other contributions for multivariate volatility models using a) finite mixture and regime-switching models and b) time-varying models (relying on the approach of local stationarity). Our contributions to modelling will cover the range from parametric to non-parametric models, based on the observation that existing parametric multivariate volatility models are not sufficiently flexible or are too heavily parameterized.

 

In particular, we will exploit our experience and combine statistical with econometric expertise in our new and original approach: inhomogeneous time series can be modelled locally in time as parametric, stationary processes. With this we capture the afore-mentioned aspect of a time-inhomogeneous economy. Hence, we recover a simple and attractive economic interpretation of the resulting non-parametric estimators which have the advantage to be more robust to misspecification. As their accuracy is usually lower than that of parametric estimators, it is actually important to decide and develop, case by case, the degree of flexibility that one wants to introduce by switching from a parametric to a semi-parametric or fully non-parametric approach. We believe that with this project we present a quite comprehensive and promising research avenue that brings together researchers with a broad experience in these three areas.

 

To meet the challenge of the curse of dimensionality in multivariate time series modelling, we shall use, among others, dynamic latent variables in factor-type models. Dynamic latent variables can be interpreted as time-varying parameters, and they can be modelled as a complex lower dimensional dynamic system. Models can be more parsimonious in parameters through latent variables whose number is smaller than the number of modelled time series. More specifically, in our proposed research agenda we try to find optimal solutions in that an appropriately chosen subset of such "time-varying parameters" will at the same time allow sufficient parsimony on one hand, without losing too much flexibility on the other hand. Finding the correct subset in view of its meaningful economic interpretation puts this aspect of our research proposal beyond a pure statistical question.