Correlation at First Sight

Abstract

The synthetic collateralized debt obligation (CDO) market has, over the last year, seen a significant increase in liquidity and transparency. The availability of published prices such as TracX and iBoxx tranches permits the calibration of model parameters, which was not achievable a year ago. This paper details what we believe has become the market standard approach in CDO valuation. The valuation model is introduced and analysed in depth to develop a better practical understanding of its use and the implications of parameter selection and calibration. In particular, we examine the idea that correlation within a copula model can be seen to be an equivalent measure to volatility in a standard B&S option framework and, correspondingly, we seek to calibrate smile and skew.(J.E.L.: G13).

On the Mechanism of CDOs behind the Current Financial Crisis and Mathematical Modeling with Levy Distributions

“…In one line of thinking, to relax the assumption of Gaussian distribution in the one factor Gaussian copula model, student-t copula [5][6][7][8][9][10][11][12], double-t copula [13,14], Clayton copula [12,[15][16][17][18][19][20], Archimedian copula [21,22], Marshall Olkin copula [23][24][25][26] are studied. And default correlations are made stochastic and correlated with the systematic factor in [27,28] to relax the assumption that default correlations are constant through time and independent of the firms default probabilities.…”

Universal approximation of credit portfolio losses using Restricted Boltzmann Machines

“…A substantial amount of research has focused on addressing these concerns by identifying alternative parametric families that are believed to be better suited for credit risk applications. So, for instance, the one-factor Gaussian copula in [61] has been superseded by stochastic correlations models [3,80], t copula models [4,21,62,32,43,66,81], double t copula models [54,17], Clayton copula models [83,82,78,64,34], Marshall-Olkin copula models [23,61,90,27,37,63], more general Archimedean copulas [72,36], and combinations of all the aforementioned models, via very general constructions in which pair copulas are glued together, as done in vine copulas [8,58,1,18].…”

CDO, HAME Copulas and an R Package 'CDO'

“…Rogge [23], the Marshall Olkin copula model in Lindskog and McNeil [11], Duffie and Singleton [24] and Giesecke [25], the double-t copula model in Hull and White [26], the Model Literature Multi-Parameter Gaussian Copula Model Hofert and Scherer [8], Hofert [9],Choros-Tomczyk et al [10] Student-t Copula Model Lindskog and McNeil [11], Embrechts et al [12] Frey and McNeil [7], Andersen et al [13] Greenberg et al [14], Mashal et al [15] Demarta and McNeil [16], Schloegl and O'Kane [17] Clayton Copula Model Schoenbucher and Schubert [18], Lindskog and McNeil [11] Schoenbucher [19], Rogge and Schoenbucher [20] Gregory and Laurent [21], Gregory and Laurent [22] Friend and Rogge [23] Marshall Olkin Copula Model Lindskog and McNeil [11], Duffie and Singleton [24] Giesecke […”