June 15, 2016 @ 5:00 pm – 6:30 pm
Aula Máxima de Derecho. Claustro de San Agustín.

Heterogeneous Archimedean copula and t-copula in credit portfolio modeling
Ludger Overbeck*, University of Giessen
Besides its advantage in modelling tail-dependency, the main drawback of standard non-Gaussian copula is the homogeneity in the tail dependency. Several approaches to solve are meanwhile developed, hierachical copula, the grouped t-copula and the heterogeneous t-copula as recently described by Luo and Shevchenko. We will show results from a concrete implementation of a factor model using the later approach in a two step estimation procedure. In particular the effects on capital allocation will be highlighted. In the second part, we will also present how this can be extended to a wide class of Archimedean copula, in order to capture heterogeneous tail-dependencies and therefore tail-sensitive capital allocation in credit portfolio models. This first part is joint work in progress with Carsten Binnenhei, Melanie Frick and Benedikt Mankel (Deka Bank).

Option-Implied Objective Measures of Market Risk
Matthias Leiss*, ETHZ; Heinrich Nax, ETHZ
Foster and Hart (2009) introduce an objective measure of the riskiness of an asset that implies a bound on how much of one’s wealth is ‘safe’ to invest in the asset while (a.s.) guaranteeing no-bankruptcy in the long run. In this study, we translate the Foster-Hart measure from static and abstract gambles to dynamic and applied finance using nonparametric estimation of risk-neutral densities from S&P 500 call and put option prices covering 2003 to 2013. This exercise results in an option-implied market view of objective riskiness. The dynamics of the resulting ‘option-implied Foster-Hart bound’ are analyzed and assessed in light of well-known risk measures in- cluding value at risk, expected shortfall and risk-neutral volatility. The new measure is shown to be a significant predictor of ahead-return downturns. Furthermore, it is able to grasp more characteristics of the risk-neutral probability distributions than other measures, furthermore exhibiting predictive consistency. The robustness of the risk-neutral density estimation method is analyzed via Monte Carlo methods.

Counterparty Risk and Funding: Immersion and Beyond
Shiqi Song*, Université d’Evry ; Stéphane Crépey, University of Evry
In Cr’epey’s paper (textsc{Cr’epey, S.} (2015). Bilateral Counterparty risk under funding constraints. Part II: CVA. textit{Mathematical Finance} textbf{25}(1), 1-50.), a basic reduced-form counterparty risk modeling approach {was introduced} under a rather standard immersion hypothesis between a reference filtration and the filtration progressively enlarged by the default times of the two parties, also involving the continuity of some of the data at default time. This basic approach is too restrictive for application to credit derivatives, which are characterized by strong wrong-way risk, i.e.~adverse dependence between the exposure and the credit riskiness of the counterparties, and gap risk, i.e.~slippage between the portfolio and its collateral during the so-called cure period that separates default from liquidation.
{This paper} shows how a suitable extension of the basic approach can be devised so that it can be applied in dynamic copula models of counterparty risk on credit derivatives.
More generally, this extended approach is applicable in any marked default time intensity setup satisfying a suitable integrability condition. The integrability condition expresses that no mass is lost in a related measure change.

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