Journal ArticleDOI
Analytical Pricing of Basket Default Swaps in a Dynamic Hull & White Framework
TLDR
In this article, the authors compared the shape of pairwise default correlations of the Hull & White, the Gaussian copula and the Mai & Scherer model with compound Poisson process as Levy subordinator.Abstract:
In this paper, some analytical results related to the Hull & White dynamic model of credit portfolio of N obligors in the case of constant jump size are provided. For instance, this specific assumption combined with the moment generating function of the Poisson process lead to analytical calibration for the model with respect to the underlying CDSs. Further, extremely simple analytical expressions are obtained for first-to-default swaps; the more general case of quantities related to nth-to-default swaps also have a closed form and remain tractable for small n. Similarly, pairwise correlation between default indicators also proves to be simple. Although the purpose of this note is not to compare models, we compare the shape of pairwise default correlations of the Hull & White, the Gaussian copula and the Mai & Scherer model with compound Poisson process as Levy subordinator. It is shown that only the models including jumps can lead to non-vanishing default correlation for short-term maturities. Further, these models can generate higher default correlation levels compared to the Gaussian one. When calibrated on default probability of first default time, Jump-based models also lead to much higher default probability for the last obligor to default. Finally, we tackle the problem of simultaneous jumps, which prevent the above class of models to be usable when recoveries are name-specific. To that end, we propose a tractable compromise to deal with baskets being non-homogeneous recovery-wise under the Hull & White model by splitting isolated and non-isolated default events.read more
Citations
More filters
Journal ArticleDOI
Sibuya copulas
Marius Hofert,Frédéric Vrins +1 more
TL;DR: Sibuya copulas as discussed by the authors are a class of copulas based on an increasing stochastic process whose Laplace-Stieltjes transform enters the copula as a parameter function.
Journal ArticleDOI
Characteristic Function of Time-Inhomogeneous Lévy-Driven Ornstein-Uhlenbeck Processes
TL;DR: In this paper, the authors derived the characteristic function (CF) of integrals of Levy-driven Ornstein-Uhlenbeck processes with time-inhomogeneous coefficients, taking the form of the exponential integral of the time-changed characteristic exponent.
Posted Content
Characteristic Functions of Integrated Gaussian and L\'evy Processes
TL;DR: In this article, the distributional properties of integrals of Markov processes with non-stationary increments have been investigated and the analytical solution to the most general form of Gaussian processes (with nonstationary increment) solving a stochastic differential equation has been provided.
References
More filters
BookDOI
Financial modelling with jump processes
Rama Cont,Peter Tankov +1 more
TL;DR: In this article, the authors provide a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists.
Book
Copula methods in finance
TL;DR: The author examines the implications of Sklar's theorem in financial applications: toward a non-Black-Scholes world for derivatives pricing, Hedging and Risk Management and the application of VaR bounds to copulas.
Journal ArticleDOI
On Default Correlation: A Copula Function Approach
TL;DR: In this paper, a copula function approach was used to specify the joint distribution of survival times after marginal distributions of survival time are derived from market information, such as risky bond prices or asset swap spreads, and the default correlation between two credit risks was defined as the correlation coefficient between their survival times.
Journal ArticleDOI
Time-Dependent Association Measures for Bivariate Survival Distributions
TL;DR: In this paper, the authors proposed time-dependent association measures for bivariate survival analysis, which provide informative summaries for data on twins, ophthalmic and auditory studies, and for other matched-pair designs.
Journal ArticleDOI
Dynamic Models of Portfolio Credit Risk: A Simplified Approach
John Hull,Alan White +1 more
TL;DR: In this paper, a dynamic process for the cumulative hazard rate for a credit portfolio, that allows discrete jumps with jump size increasing in the number of jumps, is introduced, which ties together the market quotes for CDO tranches of different maturities into a unified valuation framework.