Introducing an analytical solution and an improved one-factor gaussian copula model for the pricing of heterogeneous CDOs

Xin Gao, Binlin Wu () and Tobias Schäfer ()
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Xin Gao: Natural Sciences Department, LaGuardia Community College of The City University of New York, 31-10 Thomson Ave, Long Island City, NY 11101, USA
Binlin Wu: #x2020;Physics Department and CSCU Center for Nanotechnology, Southern Connecticut State University, 501 Crescent Street, New Haven, CT 06515, USA
Tobias Schäfer: #x2021;Department of Mathematics, College of Staten Island of The City University of New York, 2800 Victory Blvd, Staten Island, NY 10314, USA

International Journal of Financial Engineering (IJFE), 2017, vol. 04, issue 02n03, 1-17

Abstract: This paper introduced an analytical solution and improved one-factor Gaussian copula models to the pricing of tranches of a Collateralized debt obligations (CDO) portfolio. Prices of CDO tranches are calculated and compared using the analytical model and different one-factor Gaussian copula models including a two-category heterogeneous model and a completely heterogeneous model that uses individual rate parameter and correlation coefficient for each reference entity in a CDO portfolio. When correlation among reference entities is low, the price calculated from the analytical model matches very well with the one-factor Gaussian copula models. However, as the correlation among reference entities increases, prices calculated using both the analytical solution and the homogeneous or two-category one-factor Gaussian copula models significantly deviate from the completely heterogeneous one-factor Gaussian copula model. This result verifies our belief that uniform parameters cannot completely capture all the heterogeneities in a CDO portfolio. Completely heterogeneous one-factor Gaussian copula model using individual rate parameters and correlation coefficients for each reference entities provides more reliable and accurate prices for structured securities.

Keywords: CDO; Gaussian copula; pricing model; structured securities; Monte Carlo (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S2424786317500384

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