Concurrent Credit Portfolio Losses

We consider the problem of concurrent portfolio losses in two non-overlapping credit portfolios. In order to explore the full statistical dependence structure of such portfolio losses, we estimate their empirical pairwise copulas. Instead of a Gaussian dependence, we typically find a strong asymmetry in the copulas. Concurrent large portfolio losses are much more likely than small ones. Studying the dependences of these losses as a function of portfolio size, we moreover reveal that not only large portfolios of thousands of contracts, but also medium-sized and small ones with only a few dozens of contracts exhibit notable portfolio loss correlations. Anticipated idiosyncratic effects turn out to be negligible. These are troublesome insights not only for investors in structured fixed-income products, but particularly for the stability of the financial sector

A coupled parametric and nonparametric approach for modal analysis of a satellite

This study takes place in the context of dynamical prediction for satellite structures. Aims of such studies are to survey the dynamical response of satellite equipment and components, to check that requirements are correct and to give prediction of vibration levels, which are inputs for the experimental test validation according to the launcher specification. This prediction is done by modal analysis performed on a numerical model built by finite element method. Uncertainties on equipment and components properties lead to random frequency response function (FRF). This paper aims at understanding how modal approach can be adapted to probabilistic framework in order to calculate cumulative density function or, at least, some quantiles of a FRF. Starting point of deterministic modal analysis is the study of a single degree of freedom (DOF) system. C. Heinkelé analytically expresses the probability density function (PDF) of the FRF of an oscillator with a random natural pulsation following a uniform law. We have generalized this work to random natural pulsation following a law of finite variance. Then, the expression of a FRF between two DOF of the structure is a linear function of random oscillators FRF and DOF components of random eigenvectors. Assuming that random eigenvectors are close to their means, we have access to the characteristic function of the random FRF between two DOF as a multi-dimensional integral with respect to the joint PDF of the oscillators FRF. This paper mainly focuses on two major points which are calculation of oscillators joint PDF and inversion of characteristic functions. The first one is tackled by copulas theory. Dependence structure of random eigenvalues are identified and modeled by a copula. Then we apply results on copulas transformations to obtain joint PDF of oscillators FRF. Classical results concern monotonic transformations but we extended these ones to non-monotonic cases. Concerning inversion of characteristic function, several methods are studied to numerically compute the Gil-Pelaez formula. This approach allows to access some FRF quantiles by numerical integration which error can be controlled. Moreover, an interesting point is the flexibility in the identification of the random eigenvalues PDF. This is especially interesting in order to couple parametric identification with nonparametric one, when only few dispersion informations are given for equipments, housed in the satellite primary structure

A study of dependency features of spike trains through copulas

Simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. Discerning the presence of direct links between neuron from data is still a not completely solved problem. To enlarge the number of tools for detecting the underlying network structure, we propose here the use of copulas, pursuing on a research direction we started in [1]. Here, we adapt their use to distinguish different types of connections on a very simple network. Our proposal consists in choosing suitable random intervals in pairs of spike trains determining the shapes of their copulas. We show that this approach allows to detect different types of dependencies. We illustrate the features of the proposed method on synthetic data from suitably connected networks of two or three formal neurons directly connected or influenced by the surrounding network. We show how a smart choice of pairs of random times together with the use of empirical copulas allows to discern between direct and un-direct interactions

Copula based simulation procedures for pricing basket Credit Derivatives

This paper deals with the impact of structure of dependency and the choice of procedures for rare-event simulation on the pricing of multi-name credit derivatives such as nth 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 basket default swaps and CDO under different structure of dependency and assessing the influence of different price drivers (correlation, hazard rates and recovery rates) on modelling portfolio losses. Gaussian copulas and Monte Carlo simulation is widely used to measure the default risk in basket credit derivatives. Default risk is often considered as a rare-event and then, many studies have shown that many distributions have fatter tails than those captured by the normal distribution. Subsequently, the choice of copula and the choice of procedures for rare-event simulation govern the pricing of basket credit derivatives. An alternative to the Gaussian copula is Clayton copula and t-student copula under importance sampling procedures for simulation which captures the dependence structure between the underlying variables at extreme values and certain values of the input random variables in a simulation have more impact on the parameter being estimated than others .Collateralized Debt Obligations, Basket Default Swaps, Monte Carlo method, One factor Gaussian copula, Clayton copula, t-student copula, importance sampling

Real Option Valuation of a Portfolio of Oil Projects

Various methodologies exist for valuing companies and their projects. We address the problem of valuing a portfolio of projects within companies that have infrequent, large and volatile cash flows. Examples of this type of company exist in oil exploration and development and we will use this example to illustrate our analysis throughout the thesis. The theoretical interest in this problem lies in modeling the sources of risk in the projects and their different interactions within each project. Initially we look at the advantages of real options analysis and compare this approach with more traditional valuation methods, highlighting strengths and weaknesses ofeach approach in the light ofthe thesis problem. We give the background to the stages in an oil exploration and development project and identify the main common sources of risk, for example commodity prices. We discuss the appropriate representation for oil prices; in short, do oil prices behave more like equities or more like interest rates? The appropriate representation is used to model oil price as a source ofrisk. A real option valuation model based on market uncertainty (in the form of oil price risk) and geological uncertainty (reserve volume uncertainty) is presented and tested for two different oil projects. Finally, a methodology to measure the inter-relationship between oil price and other sources of risk such as interest rates is proposed using copula methods.Imperial Users onl