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The IUP Journal of Applied Finance
Impact of Stochastic Correlation on CDO Pricing
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In CDO pricing, the cross-correlation coefficients play a significant role as it is the sole parameter used. Criticisms are levelled around two features of these correlation coefficients: a dependable data is not available to compute the correlation coefficients between reference obligors; and the same coefficients are used across firms and over the entire life of the CDO while computing the survival, default and hazard probabilities. This strong assumption creates correlation smile and the resultant price is a crude approximation. In this paper, we have attempted to capture the sensitivity of the correlation coefficients in the pricing of CDOs and have also attempted to relax the assumption of the constant correlation coefficients by taking simulated random cross-correlation coefficients to study the effect on pricing. Our results show that the cross-correlation coefficients affect only the premium leg payments and play insignificant role in default leg payment, accrued premium and default losses. When correlation coefficient increases, the premium payable also increases, but at a decreasing rate. If stochastic correlation coefficients are applied, the premium leg and default amounts show a stable pattern, while default payment slightly increases when compared to fixed correlation coefficients.

 
 
 

The current hotly debated issue is the financial turmoil in large banks around the world that sparked the global financial crisis. The respective governments, to protect their economies and financial systems, utilize taxpayers' money in the name of reconstruction to bail out the problematic banks. The banking crisis had caused major job loss and its ancillary problems associated with the poor performance of individual national economies. The policy of non-intervention, market-driven economy, self-regulatory process and lack of transparency pushed the financial system of almost all countries to the brink of collapse. The economic problems are not severe for over-regulated and strict economies' financial systems; however, the strong under-regulated economies were badly affected. The problem emanated primarily from two sources—the subprime lending and the reckless creation and unregulated trading of Collateralized Debt Obligations (CDOs). In subprime lending, the credit quality and repaying capacity of the borrower took a back seat, without proper assessment, where the bankers lent loans believing in the future appreciation of property price. In the event of borrowers' default, the banks were confident of selling the collateral at a decent price; thus, the loan was always deemed safe. The above premise is true when a few individual borrowers fail to repay the loan. However, if several borrowers simultaneously fail to repay, the credit risk increases several fold due to the existence of correlation risk. The correlation risk is the main cause of the crisis that banks and financial institutions around the globe face today.

The second cause of crisis is the regulatory measures proposed by Basel II. The Basel II mandates all banks to keep adequate Tier I capital to meet any credit risk arising from financial assets created by them. To avoid Tier I capital and to minimize credit risk from lending, the commercial banks issued structured financial products through a specially created Special Purpose Vehicle (SPV). Table 1 provides operational details of banks that sell asset-backed securities through their own SPVs to transfer risk and to get liquidity. In fact, the banks buy protection against portfolio of its financial assets (loans and bonds). The banks pay regular premium to the investors (protection sellers), quarterly or semi-annually. Investors receive premium from SPVs and bear losses when credit event occurs. The investors are none other than the institutional investors and banks of different countries.

 
 
 

Applied Finance Journal, Stochastic Correlation, CDO Pricing, Financial Systems, Collateralized Debt Obligations, Financial Products, Financial Assets, Commercial Banks, Credit Risks, Structural Model, Poisson Process, WorldCom Corporations, Distributed Gaussian Probabilities.