3,153 research outputs found
Unsupervised Domain Adaptation with Copula Models
We study the task of unsupervised domain adaptation, where no labeled data
from the target domain is provided during training time. To deal with the
potential discrepancy between the source and target distributions, both in
features and labels, we exploit a copula-based regression framework. The
benefits of this approach are two-fold: (a) it allows us to model a broader
range of conditional predictive densities beyond the common exponential family,
(b) we show how to leverage Sklar's theorem, the essence of the copula
formulation relating the joint density to the copula dependency functions, to
find effective feature mappings that mitigate the domain mismatch. By
transforming the data to a copula domain, we show on a number of benchmark
datasets (including human emotion estimation), and using different regression
models for prediction, that we can achieve a more robust and accurate
estimation of target labels, compared to recently proposed feature
transformation (adaptation) methods.Comment: IEEE International Workshop On Machine Learning for Signal Processing
201
Copulas and Dependence models in Credit Risk: Diffusions versus Jumps
The most common approach for default dependence modelling is at present copula functions. Within this framework, the paper examines factor copulas, which are the industry standard, together with their latest development, namely the incorporation of sudden jumps to default instead of a pure diffusive behavior. The impact of jumps on default dependence - through factor copulas - has not been fully explored yet. Our novel contribution consists in showing that modelling default arrival through a pure jump asset process does matter, even when the copula choice is thestandard, factor one, and the correlation is calibrated so as to match the diffusive and non diffusive case. An example from the credit derivative market is discussed.credit risk, correlated defaults, structural models, Lévy processes, copula functions, factor copula
Option Valuation in Multivariate SABR Models
We consider the joint dynamic of a basket of n-assets where each asset itself follows a SABR stochastic volatility model. Using the Markovian Projection methodology we approximate a univariate displaced diffusion SABR dynamic for the basket to price caps and floors in closed form. This enables us to consider not only the asset correlation but also the skew, the cross-skew and the decorrelation in our approximation. The latter is not possible in alternative approximations to price e.g. spread options. We illustrate the method by considering the example where the underlyings are two constant maturity swap (CMS) rates. Here we examine the influence of the swaption volatility cube on CMS spread options and compare our approximation formulae to results obtained by Monte Carlo simulation and a copula approach.SABR; CMS spread; displaced diffusion; Markovian projection; GyÄongy Lemma
Efficient estimation of parameters in marginals in semiparametric multivariate models
Recent literature on semiparametric copula models focused on the situation when the marginals are specified nonparametrically and the copula function is given a parametric form. For example, this setup is used in Chen, Fan and Tsyrennikov (2006) [Efficient Estimation of Semiparametric Multivariate Copula Models, JASA] who focus on efficient estimation of copula parameters. We consider a reverse situation when the marginals are specified parametrically and the copula function is modelled nonparametrically. This setting is no less relevant in applications. We use the method of sieve for efficient estimation of parameters in marginals, derive its asymptotic distribution and show that the estimator is semiparametrically efficient. Simulations suggest that the sieve MLE can be up to 40% more efficient relative to QMLE depending on the strength of dependence between the marginals. An application using insurance company loss and expense data demonstrates empirical relevance of this setting.
Max-stable models for multivariate extremes
Multivariate extreme-value analysis is concerned with the extremes in a
multivariate random sample, that is, points of which at least some components
have exceptionally large values. Mathematical theory suggests the use of
max-stable models for univariate and multivariate extremes. A comprehensive
account is given of the various ways in which max-stable models are described.
Furthermore, a construction device is proposed for generating parametric
families of max-stable distributions. Although the device is not new, its role
as a model generator seems not yet to have been fully exploited.Comment: Invited paper for RevStat Statistical Journal. 22 pages, 3 figure
Generalized Logistic Models and its orthant tail dependence
The Multivariate Extreme Value distributions have shown their usefulness in
environmental studies, financial and insurance mathematics. The Logistic or
Gumbel-Hougaard distribution is one of the oldest multivariate extreme value
models and it has been extended to asymmetric models. In this paper we
introduce generalized logistic multivariate distributions. Our tools are
mixtures of copulas and stable mixing variables, extending approaches in Tawn
(1990), Joe and Hu (1996) and Foug\`eres et al. (2009). The parametric family
of multivariate extreme value distributions considered presents a flexible
dependence structure and we compute for it the multivariate tail dependence
coefficients considered in Li (2009)
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