Minimally cross-entropic conditional density : a generalization of the GARCH model

The stylized fact of time-varying volatility in financial series is commonly accepted amongst scholars as well as practitioners. The GARCH model has been exceptionally successful in this area. Our approach, the minimally cross-entropic conditional density (MCECD) model, is a generalization of GARCH(1,1) which can cope with conditional skewness and kurtosis. It is so-named because the parameter updating method is based on cross-entropy minimization rather than autoregression

Chiral perturbation theory

Chiral perturbation theory (ChPT) is an effective field theory that describes the properties of strongly-interacting systems at energies far below typical hadron masses. The degrees of freedom are hadrons instead of the underlying quarks and gluons. ChPT is a systematic and model-independent approximation method based on an expansion of amplitudes in terms of light-quark masses and momenta. The following is a brief overview of ChPT that is largely based on Scherer, Schindler, Lect. Notes Phys. 830 (2012), which can be referred to for a more detailed introduction.Comment: contribution to the review "50 Years of Quantum Chromodynamics," edited by F. Gross and E. Klempt [arXiv:2212.11107], to be published in EPJ

Modeling the evolution of implied CDO correlations

CDO tranche spreads (and prices of related portfolio-credit derivatives) depend on the market's perception of the future loss distribution of the underlying credit portfolio. Applying Sklar's seminal decomposition to the distribution of the vector of default times, the portfolio-loss distribution derived thereof is specified through individual default probabilities and the dependence among obligors' default times. Moreover, the loss severity, specified via obligors' recovery rates, is an additional determinant. Several (specifically univariate) credit derivatives are primarily driven by individual default probabilities, allowing investments in (or hedging against) default risk. However, there is no derivative that allows separately trading (or hedging) default correlations; all products exposed to correlation risk are contemporaneously also exposed to default risk. Moreover, the abstract notion of dependence among the names in a credit portfolio is not directly observable from traded assets. Inverting the classical Vasicek/Gauss copula model for the correlation parameter allows constructing time series of implied (compound and base) correlations. Based on such time series, it is possible to identify observable variables that describe implied correlations in terms of a regression model. This provides an economic model of the time evolution of the market's view of the dependence structure. Different regression models are developed and investigated for the European CDO market. Applications and extensions to other markets are discusse

Exchangeable min-id sequences: Characterization, exponent measures and non-decreasing id-processes

We establish a correspondence between exchangeable sequences of random variables whose finite-dimensional distributions are min- (or max-) infinitely divisible and non-negative, non-decreasing, infinitely divisible stochastic processes. The exponent measure of a min-id sequence is shown to be the sum of a very simple "drift measure" and a mixture of product probability measures, which corresponds uniquely to the L\'evy measure of a non-decreasing infinitely divisible process. The latter is shown to be supported on non-negative and non-decreasing functions. Our results provide an analytic umbrella which embeds the de Finetti subfamilies of many classes of multivariate distributions, such as exogenous shock models, exponential and geometric laws with lack-of-memory property, min-stable multivariate exponential and extreme-value distributions, as well as reciprocal Archimedean copulas with completely monotone generator and Archimedean copulas with log-completely monotone generator.Comment: 53 pages, 3 Figure