Abstract
The study extends the theoretical framework proposed to decompose rating migration matrices from bond market price data. In this context, method to decompose default probability term structures for and from interest rate term structures for different rating categories, is also delineated and empirically evaluated. In principle, whenever it is possible to decompose an interest rate term structure for a rating category from ahistorical market data, it should also be possible to decompose a default probability term structure for the rating category, and to decompose a default probability term structure for the particular interest rate term structure of the rating category. Principal to the method and vantage point is that, when decomposing a default probability term structure, purely ahistorical market data is used, as is the case when decomposing interest rate term structures. In addition, greater emphasis is placed on surfacing actual market perceptions regarding default probability, which may differ from theoretical modelling of default probability. The method naturally allows a mapping and transitioning between interest rate term structures and default probability term structures. Consequentially, the study examines the corresponding interest rate term structures of the default probability term structures of a typical rating migration matrix, and the corresponding default probability term structures of a typical market interest rate term structure set. The sensitivity of the results to the coupon rate used is also examined, particularly in view of using an external (artificial) portfolio to facilitate the process. It is found that the default probability term structures decomposed from market interest rate term structures significantly differ from rating migration matrix based default probability term structures. This may point to differing views on default probability term structures. In addition, it is also shown that even external (artificial) portfolios can illuminate the default probability term structures of interest rate term structures with reasonable accuracy. Mapping to and fro interest rate term structures and default probability term structures introduces and additional level of triangulation and evaluation. It is expected that interest rate term structures should have valid and sensible default probability term structures, and vice versa. Another important implication of decomposing default probability term structures from ahistorical market data is that the default probability term structures would change at the frequency of the market and market data. This implies that market based default probability term structures may include a volatility component. Market based ahistorical default probability term structures offer a different and unique perspective on default probability term structures. If found to be an accurate representation of market views and perceptions, it may demand a reconsideration of the prominence of default probability as a bond valuation factor.
Highlights
IntroductionThe approach allows the default risk associated with a given credit rating to change as the economy moves through different points in the business cycle
Their premise is that point-in-time methodologies that account for business cycles should provide more realistic credit risk measures than through-the-cycle models that smooth out transitory fluctuations in economic fundamentals
The study examines the default probability term structures of interest rate term structures, firstly those obtained from the previous step – mapping the interest rate term structures obtained from the default probability term structures of the rating migration matrix back to default probability term structures – and secondly a typical market interest rate term structure set
Summary
The approach allows the default risk associated with a given credit rating to change as the economy moves through different points in the business cycle They mention a body of research linking portfolio credit risk with macroeconomic factors showing, for instance, that default risk tends to increase during economic downturns. Their premise is that point-in-time methodologies that account for business cycles should provide more realistic credit risk measures than through-the-cycle models that smooth out transitory fluctuations (perceived as random noise) in economic fundamentals
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