As the world experiences the precarious operating activities of major financial institutions and household company names, the need for comprehensive understanding of default correlation has become increasingly important. By creating various modeling techniques Professor Yue Kuen Kwok at the Hong Kong University of Science and Technology, Mathematics Department and his research team examined the impact of default correlation and related implications.

"Default correlation happens when the collapse of one company or financial institution has a knock on effect and brings down others," said Professor Kwok. Also known as a parent and child relationship, the Professor said a default event could take place in a particular industry sector, as part of a supply chain event or a series of events covering a geographical area, such as Asia experienced during the 1990’s Asian financial crisis.

"Default correlation examines how the likelihood of default changes over time with the infectious effect of a institution or company that owes debt to another individual or company (the creditor), as a result of borrowing or issuing securitised investments," said the Professor. "The analysis explores how the correlated default structures among the protection seller and the reference entity affect the swap rate in credit default swaps," he added.

The dependence of firms on the general economic environment induces dependence between firms' defaults. Another source of default correlation is the borrower-lender or parent-subsidiary structures that provide the direct contagion of financial distress from one firm to another.

"The financial tsunami we are currently experiencing has highlighted the need to investigate and understand default correlation," Professor Kwok said. Understanding default correlation is important for investors and rating agencies such Standards and Poor's (S&P) and Moody's. The understanding of the correlation between default events is also of importance to portfolio management and valuation of credit-sensitive instruments.

Explaining his research techniques, Professor Kwok said in conjunction with his research team he performed the valuation of a credit default swap with counterparty risk using the reduced form framework with inter-dependent default correlation. "We formulated the Markov chains framework of the interacting intensities model and used it to derive the joint density of default times of risky obligors," said the Professor.

Professor Kwok applied the contagion model to analyse the counterparty risk of a credit default swap when both the protection seller and the reference obligor are subject to a common shock. "We analysed how the settlement risk and the replacement cost affect the swap rate in credit default swaps," said Professor Kwok. The term structures of default correlation were also analysed using correlation measures, including the Spearman Rho coefficient and the linear correlation coefficient. Spearman Rho coefficient is used to estimate strength and direction of association between two ordinal level variables while linear correlation coefficient measures the strength and the direction of a linear relationship between two variables.

Professor Kwok and his research team also examined which default correlation measures have better descriptive power. They also looked at the way inter-dependent default risk structure between the protection seller and the reference entity in a credit default swap affects the swap premium. "We also carried out research to quantify the discount on the swap premium with regard to the settlement risk if the protection seller cannot fulfill its obligation to make compensation payment at the end of the settlement period," said the Professor. His team also addressed the issue of how to estimate the replacement cost due to counterparty risk, which is the excess premium required to enter a new contract upon the default of the protection seller.

Professor Yue Kuen Kwok
Department of Mathematics
The Hong Kong University of Science and Technology
maykwok@ust.hk