1,720,974 research outputs found
Mixing and moments properties of a non-stationary copula-based Markov process
Full text linkWe provide conditions under which a non-stationary copula-based Markov process is geometric beta-mixing and geometric rho-mixing. Our results generalize some results of Beare who considers the stationary case. As a particular case we introduce a stochastic process, that we call convolution-based Markov process, whose construction is obtained by using the C-convolution operator which allows the increments to be dependent. Within this subclass of processes we characterize a modified version of the standard random walk where copulas and marginal distributions involved are in the same elliptical family. We study mixing and moments properties to identify the differences compared to the standard case
Extensions and distortions of λ-fuzzy measures
Full text linkWe propose extensions and distorsion techniques to improve the flexibility of λ-fuzzy measures. As for extensions, we suggest to use the family of Archimedean t-conorms as generators of the fuzzy measures. As for distortions, we propose the composition or patchwork of different generators. As an example of application, we show that in option pricing these techniques substantially improve the flexibility of the model to reproduce features observed from market data that only one Archimedean generator would not be able to represent
Functional convergence of Snell envelopes: applications to American Options approximations
No full textHierarchical Archimedean Dependence in Common Shock Models
Full text linkIn this paper we show how to extend a simple common shock model with Archimedean dependence of the hidden variables to the non-exchangeable case. The assumption is that the hidden risk factors are linked by a hierarchical Archimedean dependence structure, possibly fully nested. We give directions about how to implement the model and to address the issue that the hidden variables must be put in descending dependence order. We show how the model can be simplified in the Gumbel-Marshall-Olkin distribution in Cherubini and Mulinacci (2017), the only case in which exponential distribution of the observed variables is preserved
Convolution Copula Econometrics
No full textThis book presents a novel approach to time series econometrics, which studies the behavior of nonlinear stochastic processes. This approach allows for an arbitrary dependence structure in the increments and provides a generalization with respect to the standard linear independent increments assumption of classical time series models. The book offers a solution to the problem of a general semiparametric approach, which is given by a concept called C-convolution (convolution of dependent variables), and the corresponding theory of convolution-based copulas. Intended for econometrics and statistics scholars with a special interest in time series analysis and copula functions (or other nonparametric approaches), the book is also useful for doctoral students with a basic knowledge of copula functions wanting to learn about the latest research developments in the field
An integro-differential variational inequality and the pricing of American options in a jump-diffusion model: bounds and stabilty
No full textRyu-type extended Marshall-Olkin model with implicit shocks and joint life insurance applications
Full text linkIn this paper we suggest an improvement of the Extended Marshall-Olkin methodology by allowing an
implicit effect of the common shocks affecting the elements of the system. Properties of this new model
are studied. We propose an empirical application to a sample of censored residual lifetimes of couples of
insureds extracted from a data set of annuities contracts of a large Canadian life insurance company. We
obtain estimation of the model parameters using a two-stage maximum likelihood technique and discuss
the obtained results.In this paper we suggest an improvement of the Extended Marshall-Olkin methodology by allowing an implicit effect of the common shocks affecting the elements of the system. Properties of this new model are studied. We propose an empirical application to a sample of censored residual lifetimes of couples of insureds extracted from a data set of annuities contracts of a large Canadian life insurance company. We obtain estimation of the model parameters using a two-stage maximum likelihood technique and discuss the obtained results
Marshall–Olkin Distributions: Advances in Theory and Applications
No full textThis book presents the latest advances in the theory and practice of Marshall-Olkin distributions. These distributions have been increasingly applied in statistical practice in recent years, as they make it possible to describe interesting features of stochastic models like non-exchangeability, tail dependencies and the presence of a singular component. The book presents cutting-edge contributions in this research area, with a particular emphasis on financial and economic applications. It is recommended for researchers working in applied probability and statistics, as well as for practitioners interested in the use of stochastic models in economics. This volume collects selected contributions from the conference “Marshall-Olkin Distributions: Advances in Theory and Applications,” held in Bologna on October 2-3, 2013
Dynamic copula methods in Finance
No full textThis book introduces readers to the use of copula functions to represent the dynamics of financial assets and risk factors, integrated temporal and cross-section applications. The first part of the book will briefly introduce the standard the theory of copula functions, before examining the link between copulas and Markov processes. It will then introduce new techniques to design Markov processes that are suited to represent the dynamics of market risk factors and their co-movement, providing techniques to both estimate and simulate such dynamics. The second part of the book will show readers how to apply these methods to the evaluation of pricing of multivariate derivative contracts in the equity and credit markets. It will then move on to explore the applications of joint temporal and cross-section aggregation to the problem of risk integration
Time-varying dependence and currency tail risk during the Covid-19 pandemic
Full text linkPurpose: The purpose of this paper is to introduce a generalization of the time-varying correlation elliptical copula models and to analyse its impact on the tail risk of a portfolio of foreign currencies during the Covid-19 pandemic. Design/methodology/approach: The authors consider a multivariate time series model where marginal dynamics are driven by an autoregressive moving average (ARMA)–Glosten-Jagannathan-Runkle–generalized autoregressive conditional heteroscedastic (GARCH) model, and the dependence structure among the residuals is given by an elliptical copula function. The correlation coefficient follows an autoregressive equation where the autoregressive coefficient is a function of the past values of the correlation. The model is applied to a portfolio of a couple of exchange rates, specifically US dollar–Japanese Yen and US dollar–Euro and compared with two alternative specifications of the correlation coefficient: constant and with autoregressive dynamics. Findings: The use of the new model results in a more conservative evaluation of the tail risk of the portfolio measured by the value-at-risk and the expected shortfall suggesting a more prudential capital allocation policy. Originality/value: The main contribution of the paper consists in the introduction of a time-varying correlation model where the past values of the correlation coefficient impact on the autoregressive structure. © 2023, Emerald Publishing Limited
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