In single-obligor default risk modelling, using a background filtration in conjunction with a suitable embedding hypothesis (generally known as H-hypothesis or immersion property) has proven a very successful tool to separate the actual default event from the model for the default arrival intensity. In this paper we analyze the conditions under which this approach can be extended to the situati...

Among the most crucial input parameters for credit portfolio risk models are the co-movements of default risks. Due to limited empirical evidence about the magnitude of correlations the New Basel Capital Accord sets standard requirements for calculating regulatory capital requirements, e.g. in the Consultative Document as of April 2003 asset correlations for sovereigns, banks and corporates bet...

The pricing of collateralized debt obligations and other basket credit derivatives is contingent upon (i) a realistic modeling of the firms’ default times and the correlation between them, and (ii) efficient computational methods for computing the portfolio loss distribution from the individual firms’ default time distributions. Factor models, a widelyused class of pricing models, are computati...

We propose a reduced form model for default that allows us to derive closed-form solutions to all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and probabilities of survival. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity is allow...

Consider a portfolio of n obligors such as loans, corporate bonds and other instruments subject to possible default. Tang and Yuan (2012, Submitted) introduced a new model for the loss given default and studied its tail behavior, Value at Risk, and Conditional Tail Expectation under the assumption that the losses jointly follow a multivariate regularly varying distribution. However, in the case...

We develop a model for pricing derivative and hybrid securities whose value may depend on different sources of risk, namely, equity, interestrate, and default risks. In addition to valuing such securities the framework is also useful for extracting probabilities of default (PD) functions from market data. Our model is not based on the stochastic process for the value of the firm, which is unobs...

Correlated defaults and systemic risk are clearly priced in credit portfolio securities such as CDOs or index CDSs. In this paper we study an extensive CDX data set for evidence whether correlated defaults are also present in the underlying CDS market. We develop a cash flow based top-down approach for modeling CDSs from which we can derive the following major contributions: (I) Correlated defa...

Default Probabilities quantitatively measures the credit risk that a borrower will be unable or unwilling to repay its debt. An accurate model estimate, as function of time, these default probabilities is crucial importance in derivatives market. In this work, we adapt Merton’s [1] original works on risk, consumption and portfolio rules an individual wealth scenario, apply it compute probabilit...

On computational methods for the valuation of credit derivatives Wanhe Zhang Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2010 A credit derivative is a financial instrument whose value depends on the credit risk of an underlying asset or assets. Credit risk is the possibility that the obligor fails to honor any payment obligation. This thesis proposes four ...

The multivariate modelling of default risk is a crucial aspect of the pricing of credit derivative products referencing a portfolio of underlying assets, and the evaluation of Value at Risk of such portfolios. This paper proposes a model for the joint dynamic behavior of credit ratings for several …rms. Namely, individual credit ratings are modelled by univariate continuous time Markov chain, w...