Dynamic Copula Processes

• Quem: Margaret Armstrong and Alain Galli
• Onde: FGV - Praia de Botafogo, 190, room 317
• Quando: 23 de Outubro de 2014 às 16:00h

The standard way of modelling several stochastic processes which are not mutually independent is as correlated components of a Gaussian process (that is, normally distributed). It is easy to generalize this to elliptic processes with distributions like students t. There are two problems with this approach: firstly, all the variables must have the same marginal distribution and secondly, the correlation structure (in the wide sense) is symmetrical in the upper and lower tails (left figure below). But in reality, some variables are upper tail dependent (or lower tail) as in right figure below.

Copulas were invented to provide a much wider range of “correlation” structures between variables & to allow variables to have different marginal distributions. While many bivariate copulas exist, it is more difficult to construct multivariate ones, and it is even more difficult to construct dynamic copula processes.

This paper presents a flexible family of copula-based multivariate models designed for handling large numbers of variables (1) as random vectors in the static case or (2) as vector stochastic processes in the dynamic case. The family includes models with upper and lower tail dependence. Variables need not be exchangeable. To illustrate the model’s potential; three radically different examples have been constructed: a straight additive model, an additive conditional gamma model and a switching model. Archimedean copulas turn out to be a special case of the general model. Another advantage of these models it that it is easy to construct dynamic versions of the static copulas. Lastly, as these models are defined in a conditional independence framework, they are easy to simulate.

Paper is available on SSRN.

Speakers

Margaret Armstrong and Alain Galli started the Quantitative Finance Group at the École des Mines de Paris in 2001. The group trains French engineers who want to be quants, traders & structurers in banks. The group’s research focuses on:

• Modeling commodities (electricity, oil and gas, CO2 etc).
• Modeling the structure of electricity markets, and the impact of the introduction of renewables (wind power) and electric vehicles on day-ahead electricity prices.
• Evaluating and optimising of projects such as mines, oil fields and power plants that are subject to technical and financial uncertainty.
• Modelling the term structure of interest rates.
• Stochastic volatility models.
• Dynamic hedging of physical commitments.
• Copulas, especially Archimedean copulas.

Margaret Armstrong is a professor at the Cerna, Mines-Paristech. She has a masters in mathematical statistics from the University of Queensland, Australia, and a PhD in geostatistics from the École des Mines de Paris.

Alain GALLI is a professor at the Cerna, Mines-Paristech. He holds a PhD in mathematics from the University of Grenoble, France.

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