Copula models have become very popular and well studied among the scientific community. Now, most academic researchers, engineers, modelers, etc, own at least some basic copula toolkit and are able to apply it in real situations. Based on the famous Sklar’s theorem (Sklar 1959), copulas allow to put in place the fruitful idea of splitting the specification of a multivariate model into two parts...

Any multivariate density can be decomposed through successive conditionings into basic building blocks involving only pairs of variables. The various ways in which this can be done are called regular vines; C-vines and D-vines are prime examples of such structures. A pair-copula construction (PCC) is a modelling strategy in which conditional and unconditional bivariate copula densities are assi...

The Gaussian factor copula model is the market standard model for multi-name credit derivatives. Its main drawback is that factor copula models exhibit correlation smiles when calibrating against market tranche quotes. To overcome the calibration deficiency, we introduce a multi-period factor copula model by chaining one-period factor copula models. The correlation coefficients in our model are...

This paper deals with the impact of structure of dependency and the choice of procedures for rareevent simulation on the pricing of multi-name credit derivatives such as n to default swap and Collateralized Debt Obligations (CDO). The correlation between names defaulting has an effect on the value of the basket credit derivatives. We present a copula based simulation procedure for pricing baske...

stochastic programs are effective for solving long-term planning problems under uncertainty. Such programs are usually based on scenario generation model about future environment developments. In the present paper, the scenario model is developed for the case when enough data paths can be generated, but due to solvability of stochastic program the scenario tree has to be constructed. The propos...

Multivariate measures of association are considered which, in the bivariate case, coincide with the population version of Spearman’s rho. For these measures, nonparametric estimators are introduced via the empirical copula. Their asymptotic normality is established under rather weak assumptions concerning the copula. The asymptotic variances are explicitly calculated for some copulas of simple ...

This paper applies multivariate factor copula modeling methods to study the dependence relationships of exchange rates. We found that conditional on the common factors, the dependence among the chosen currencies is weakly asymmetric, and the two-factor Gaussian copula modeling hypothesis is more appropriate.

BACKGROUND An important issue in prediction modeling of multivariate data is the measure of dependence structure. The use of Pearson's correlation as a dependence measure has several pitfalls and hence application of regression prediction models based on this correlation may not be an appropriate methodology. As an alternative, a copula based methodology for prediction modeling and an algorithm...

1. Abstract For the performance measure approach (PMA) of RBDO, a transformation between the input random variables and the standard normal random variables is required to carry out the inverse reliability analysis. Since the transformation uses the joint cumulative density function (CDF) of input variables, the joint CDF should be known before carrying out RBDO. In many industrial RBDO problem...