We consider the problem of estimating the conditional quantile of a time series fYtg at time t given covariates Xt, where Xt can ei- ther exogenous variables or lagged variables of Yt . The conditional quantile is estimated by inverting a kernel estimate of the conditional distribution function,...

Portfolio selection and risk management are very actively studied topics in quantitative finance and applied statistics. They are closely related to the dependency structure of portfolio assets or risk factors. The correlation structure across assets and opposite tail movements are essential to...

Systemic risk quantification in the current literature is concentrated on market-based methods such as CoVaR(Adrian and Brunnermeier (2016)). Although it is easily implemented, the interactions among the variables of interest and their joint distribution are less addressed. To quantify systemic...

In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the copulae model the dependency structure between random variables, next we explain the...

In this paper we present a closed analytical formula for the calculation of the CoVaR (respectively Delta CoVaR), which is a macro risk measure introduced by Adrian and Brunnermeier to analyze and quantify the marginal contribution of a given financial institutions to the systemic risk. We...

It is important to incorporate diverse heavy-tailed dependency between risks in estimating economic capital. Copulas can be a useful technique to capture dependence structure where extreme events occur simultaneously. Using the sample of U.S. property liability insurance industry, we examine the...

We consider the expected shortfall of accounting values, or, mathematically speaking, of random variables that are not continuous (i. e. whose cumulative distribution function is not continuous). Acerbi and Tasche show that one has to abandon the conditional expectation in order to maintain...

This lecture is given at the University of Leonard de Vinci, in Paris, France, to students of the School of Engineer program in Finance. It is a general introduction to the understanding of building blocks of the non-gaussian world and the shortcomings of the normal paradigm when pricing and...

This study addresses real estate's riskiness from a distributional viewpoint. Several studies have found real estate returns to be best modeled with stable paretian distributions. Using NCREIF individual property returns this is confirmed, but the first application of stable distributions to...