Analytic Dynamic Factor Copula Model

SSRN Electronic Journal, 2000

It is commonly believed that Monte Carlo pricing of multi-name credit derivatives under copula factor models is too slow for applications. This paper will demonstrate that a vastly accelerated convergence can be achieved that is not instrument-specific, and so can be applied to all types of credit derivatives.

2008

The aim of this paper is to use copulas functions to capture the different structures of dependency when we deal with portfolios of dependent credit risks and a basket of credit derivatives. We first present the wellknown result for the pricing of default risk, when there is only one defaultable firm. After that, we expose the structure of dependency with copulas in pricing dependent credit derivatives. Many studies suggest the inadequacy of multinormal distribution and then the failure of methods based on linear correlation for measuring the structure of dependency. Finally, we use Monte Carlo simulations for pricing Collateralized debt obligation (CDO) with Gaussian an Student copulas.

Copula functions have proven to be extremely useful in describing joint default and survival probabilities. We overview the state of the art and point out some modelling issues, such as the choice of a speci…c copula and of the amount of dependence, as well as re-mapping of models. We also discuss how to simplify credit models using factors. The survey leads us to focus on historical versus risk neutral dependence. We present an original methodology for inferring risk neutral dependence without using a single factor, provide an application to market data and explore its impact on the fees of some credit derivatives. The …rst part of the paper is a review of the copula techniques developed so far in order to evaluate credit risk in default-no default models. The review proceeds as follows: we …rst resume some basics about structural and intensity- based models, then recall how and under which conditions two models of these classes can be re-mapped into each other, using the latent va...

Economic Notes, 2003

In this paper we apply a copula function pricing technique to the evaluation of credit derivatives, namely a vulnerable default put option and a credit switch. Also in this case, copulas enable to separate the specification of marginal default probabilities from their dependence structure. Their use is based here on no-arbitrage arguments, which provide pricing bounds and easy-to-implement super-replication strategies.

2007

This paper deals with the impact of structure of dependency and the choice of procedures for rareevent simulation on the pricing of multi-name credit derivatives such as n th 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.

2011

In the last decade, a considerable growth has been added to the volume of the credit risk derivatives market. This growth has been followed by the current financial market turbulence. These two periods have outlined how significant and important are the credit derivatives market and its products. Modelling-wise, this growth has parallelised by more complicated and assembled credit derivatives products such as m th to default Credit Default Swaps (࣭ࣝࣞ), m out of n (࣭ࣝࣞ) and collateralised debt obligation (ࣩࣝࣞ). In this thesis, the Lévy process has been proposed to generalise and overcome the Credit Risk derivatives standard pricing model's limitations, i.e. Gaussian Factor Copula Model. One of the most important drawbacks is that it has a lack of tail dependence or, in other words, it needs more skewed correlation. However, by the Lévy Factor Copula Model, the microscopic approach of exploring this factor copula models has been developed and standardised to incorporate an endless number of distribution alternatives those admits the Lévy process. Since the Lévy process could include a variety of processes structural assumptions from pure jumps to continuous stochastic, then those distributions who admit this process could represent asymmetry and fat tails as they could characterise symmetry and normal tails. As a consequence they could capture both high and low events' probabilities. Subsequently, other techniques those could enhance the skewness of its correlation and be incorporated within the Lévy Factor Copula Model has been proposed, i.e. the TABLE OF CONTENTS III

The Journal of Derivatives, 2008

We propose a simple dynamic model that is an attractive alternative to the (static) Gaussian copula model. The model assumes that the hazard rate of a company has a deterministic drift with periodic impulses. The impulse size plays a similar role to default correlation in the Gaussian copula model. The model is analytically tractable and can be represented as a binomial tree. It can be calibrated so that it exactly matches the term structure of CDS spreads and provides a good fit to CDO quotes of all maturities. Empirical research shows that as the default environment worsens default correlation increases. Consistent with this research we find that in order to fit market data it is necessary to assume that as the default environment worsens impulse size increases. We present both a homogeneous and heterogeneous version of the model and provide results on the use of the calibrated model to value forward CDOs, CDO options, and leveraged super senior transactions. *We are grateful to Moody's Investors Services for providing financial support for this research.

International Journal of Applied Management …, 2010

The aim of this paper is to study the impact of structure of dependency on the pricing of multi-name credit derivatives such as collateralised 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 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 are widely used to measure the default risk in basket credit derivatives. Many studies have shown that many distributions have fatter tails than those captured by the normal distribution. We use distributions with fat tails such as the t-student distribution. The paper has several practical implications that are of value for financial hedgers and engineers, financial regulators, central banks, and financial risk managers.

SSRN Electronic Journal, 2000

In this paper we apply a copula function pricing technique to the evaluation of credit derivatives, namely a vulnerable default put option and a credit switch. Also in this case, copulas enable to separate the specification of marginal default probabilities from their dependence structure. Their use is based here on no-arbitrage arguments, which provide pricing bounds and easy-to-implement super-replication strategies.

2007

The aim of this paper is to study the impact of structure of dependency on the pricing of multi-name credit derivatives such as collateralised 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 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 are widely used to measure the default risk in basket credit derivatives. Many studies have shown that many distributions have fatter tails than those captured by the normal distribution. We use distributions with fat tails such as the t-student distribution. The paper has several practical implications that are of value for financial hedgers and engineers, financial regulators, central banks, and financial risk managers.