2026-04-13T01:31:39Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/3775392024-12-20T11:49:47Zcom_2072_199267com_2072_4427col_2072_199862

Efficient wavelets-based valuation of synthetic CDO tranches Ortiz-Gracia, L. We present new formulae for the valuation of synthetic collateralized debt obligation (CDO) tranches under the one-factor Gaussian copula model. These formulae are based on the wavelet theory and the method used is called WA$ ^{[a,b]}$ . We approximate the cumulative distribution function (CDF) of the underlying pool by a finite combination of $ j$ th order B-spline basis, where the B-spline basis of order zero is typically called a Haar basis. We provide an error analysis and we show that for this type of distributions, the accuracy in the approximation is the same regardless of the order of the B-spline basis employed. The resulting formula for the Haar basis case is much easier to implement and performs better than the formula for the B-spline basis of order one in terms of computational time. The numerical experiments confirm the impressive speed and accuracy of the WA$ ^{[a,b]}$ method equipped with a Haar basis, independently of the inhomogeneity features of the underlying pool. The method appears to be particularly fast for multiple tranche valuation. 2020-10-14T11:05:13Z 2024-09-19T13:21:13Z 2020-10-14T11:05:13Z 2024-09-19T13:21:13Z 2020-10-14T11:05:13Z 2024-09-19T13:21:13Z 2014-01-01 info:eu-repo/semantics/preprint http://hdl.handle.net/2072/377539 eng CRM Preprints info:eu-repo/semantics/openAccess L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:http://creativecommons.org/licenses/by-nc-nd/4.0/ RECERCAT (Dipòsit de la Recerca de Catalunya)