Christophe Schinckus on how to make stable Lévy processes empirically plausible
Since the 1970s, a large variety of models have been developed to describe the evolution of financial markets. All these models assume that the market is relatively quiet and they have been developed in a specific probabilistic (Gaussian) framework in which extreme values cannot be included. Assuming an equilibrium market allows the models to be used to develop optimal hedging strategies in order to minimize the financial risk related to investments.
However, the last financial crisis showed that financial markets are highly volatile and more turbulent than the key models allow for. Since extreme values can occur on the market the development of hedging strategies is very complex and a riskless hedge cannot be developed from models that do not allow for these. By contrast, Christophe Schinckus shows that stable Lévy processes have very interesting properties for describing the behaviour in financial markets. These processes facilitate the modeling of data that includes extreme values. The statistical properties of these stable Levy processes nonetheless have several theoretical problems in empirical applications because they generate infinite variables. Without a solution to the infinite variance problem they are useless to describe the notion of risk usually associated with variance.
Christophe has reviewed the statistical solutions within econophysics to make these processes empirically plausible i.e. so they fit observations in which expected return or risk are not infinite. These analytical solutions involve specific truncations (normalization) for stable Lévy processes and provide answers to theoretical problems (infinite variables) encountered in financial economics in the 1960s and the 1970s. The real challenge of stable Levy modeling will be to develop a generalized framework in which a riskless hedging strategy would be possible.
Christophe Schinckus’s paper, “How do econophysicists make stable Lévy processes empirically plausible” has been presented at the research seminar organized by the Interdisciplinary Institute of Physics at the University of Balearic Island in Mallorca, Spain, the 18th of June 2012.