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

2017 ◽  
Vol 04 (02n03) ◽  
pp. 1750038
Author(s):  
Xin Gao ◽  
Binlin Wu ◽  
Tobias Schäfer
Keyword(s):  
Analytical Solution ◽  
Analytical Model ◽  
Correlation Coefficients ◽  
Gaussian Copula ◽  
Copula Model ◽  
Collateralized Debt Obligations ◽  
Copula Models ◽  
Heterogeneous Model ◽  
Collateralized Debt ◽  
Individual Rate

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.

Investigation for Synthetic Collateralized Debt Obligation

2006 ◽  
Vol 14 (1) ◽  
pp. 127-168
Author(s):  
Mi Ae Kim
Keyword(s):  
Default Probability ◽  
Gaussian Copula ◽  
Copula Model ◽  
Pricing Models ◽  
Hedging Strategy ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Non Gaussian ◽  
Asset Correlation ◽  
Debt Obligation

Recently, domestic market participants have a growing interest in synthetic Collateralized Debt Obligation (CDO) as a security to reduce credit risk and create new profit. Therefore, the valuation method and hedging strategy for synthetic CDO become an important issue. However, there is no won-denominated credit default swap transactions, which are essential for activating synthetic CDO transaction‘ In addition, there is no transparent market information for the default probability, asset correlation, and recovery rate, which are critical variables determining the price of synthetic CDO. This study first investigates the method of estimating the default probability, asset correlation coefficient, and recovery rate. Next, using five synthetiC CDO pricing models‘ widely used OFGC (One-Factor Non-Gaussian Copula) model. OFNGC (One-Factor Non-Gaussian Copula) model such as OFDTC (One-Factor Double T-distribution Copula) model of Hull and White (2004) or NIGC (Normal Inverse Gaussian Copula) model of Kalemanova et al.(2005), SC<Stochastic Correlation) model of Burtschell et al.(2005), and FL (Forward Loss) model of Bennani (2005), I Investigate and compare three points: 1) appropriateness for portfolio loss distribution, 2) explanation for standardized tranche spread, 3) sensitivity for delta-neutral hedging strategy. To compare pricing models, parameter estimation for each model is preceded by using the term structure of iTraxx Europe index spread and the tranch spreads with different maturities and exercise prices Remarkable results of this study are as follows. First, the probability for loss interval determining mezzanine tranche spread is lower in all models except SC model than OFGC model. This result shows that all mαdels except SC model in some degree solve the implied correlation smile phenomenon, where the correlation coefficient of mezzanine tranche must be lower than other tranches when OFGC model is used. Second, in explaining standardized tranche spread, NIGC model is the best among various models with respect to relative error. When OFGC model is compared with OFDTC model, OFOTC model is better than OFGC model in explaining 5-year tranche spreads. But for 7-year or 10-year tranches, OFDTC model is better with respect to absolute error while OFGC model is better with respect to relative error. Third, the sensitivity sign of senior tranctle spread with respect to asset correlation is sometime negative in NIG model while it is positive in other models. This result implies that a long position may be taken by the issuers of synthet.ic COO as a correlation delta-neutral hedging strategy when OFGC model is used, while a short position may be taken when NIGC model is used.

scholarly journals How financial products organize spatial networks: Analyzing collateralized debt obligations and collateralized loan obligations as “networked products”

2021 ◽  
pp. 0308518X2110296
Author(s):  
Jonathan Beaverstock ◽  
Adam Leaver ◽  
Daniel Tischer
Keyword(s):  
Financial Networks ◽  
Regulatory Regime ◽  
Collateralized Debt Obligations ◽  
The Us ◽  
Collateralized Debt Obligation ◽  
Role Based ◽  
Collateralized Debt ◽  
Collateralized Loan Obligation ◽  
Debt Obligation ◽  
Peak Value

During the 2010s, collateralized loan obligations rapidly became a trillion-dollar industry, mirroring the growth profile and peak value of its cousin—collateralized debt obligations—in the 2000s. Yet, despite similarities in product form and growth trajectory, surprisingly little is known about how these markets evolved spatially and relationally. This paper fills that knowledge gap by asking two questions: how did each network adapt to achieve scale at speed across different jurisdictions; and to what extent does the spatial and relational organization of today's collateralized loan obligation structuration network, mirror that of collateralized debt obligations pre-crisis? To answer those questions, we draw on the global financial networks approach, developing our own concept of the networked product to explore the agentic qualities of collateralized debt obligations and collateralized loan obligations—specifically how their technical and regulatory “needs” shape the roles and jurisdictions enrolled in a global financial network. We use social network analysis to map and analyze the evolving spatial and relational organization that nurtured this growth, drawing on data harvested from offering circulars. We find that collateralized debt obligations spread from the US to Europe through a process of transduplication—that similar role-based network relations were reproduced from one regulatory regime to another. We also find a strong correlation between pre-crisis collateralized debt obligation- and post-crisis collateralized loan obligation-global financial networks in both US$- and €-denominations, with often the same network participants involved in each. We conclude by reflecting on the prosaic way financial markets for ostensibly complex products reproduce and the capacity for network stabilities to produce market instabilities.

scholarly journals Profit and Risk under Subprime Mortgage Securitization

2011 ◽  
Vol 2011 ◽  
pp. 1-64 ◽  
Author(s):  
M. A. Petersen ◽  
J. Mukuddem-Petersen ◽  
B. De Waal ◽  
M. C. Senosi ◽  
S. Thomas
Keyword(s):  
Risk Mitigation ◽  
Collateralized Debt Obligations ◽  
Mortgage Loans ◽  
Main Hypothesis ◽  
Subprime Mortgage ◽  
Important Indicator ◽  
Residential Mortgage ◽  
Maturity Mismatch ◽  
Mortgage Securitization ◽  
Collateralized Debt

We investigate the securitization of subprime residential mortgage loans into structured products such as subprime residential mortgage-backed securities (RMBSs) and collateralized debt obligations (CDOs). Our deliberations focus on profit and risk in a discrete-time framework as they are related to RMBSs and RMBS CDOs. In this regard, profit is known to be an important indicator of financial health. With regard to risk, we discuss credit (including counterparty and default), market (including interest rate, price, and liquidity), operational (including house appraisal, valuation, and compensation), tranching (including maturity mismatch and synthetic) and systemic (including maturity transformation) risks. Also, we consider certain aspects of Basel regulation when securitization is taken into account. The main hypothesis of this paper is that the SMC was mainly caused by the intricacy and design of subprime mortgage securitization that led to information (asymmetry, contagion, inefficiency, and loss) problems, valuation opaqueness and ineffective risk mitigation. The aforementioned hypothesis is verified in a theoretical- and numerical-quantitative context and is illustrated via several examples.

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