Alternative measures of bond default risk: rating, profitability gap and probability of default.

Summary Default risk is the most important risk faced by a bond investor since it reflects the possibility of non-payment of a coupon or coupon and principal by the issuer. In practice, two + tools are generally used to measure it. The rating, a qualitative tool, is attributed to the issuer by agencies specialized in this activity. The yield spread, a quantitative tool, is the result of the market quotation of the loan. This research work focuses on the construction and validation of models integrating this potential issuer default using market data. Several original models are proposed in an actuarial framework or in a dynamic evolution of zero-coupon prices. In an actuarial approach, we propose an original two-parameter model allowing the construction of the term structure of default probabilities from the market prices of the short and long term debt of each issuer. In this theoretical framework, we also show a positive link between the profitability spread and the general level of interest rates. This result goes against many theoretical works (e.g. Leland and Toft (1996)). We also present an extension of the dynamic zero-coupon price evolution model of Jarrow and Turnbull (1995). In particular, the model proposed in this work allows us to consider various forms of default within a unified theoretical framework. From an empirical point of view, we propose original alternative measures to the actuarial spread (a commonly accepted measure), based on the deformation of the term structure of zero-coupon rates. Finally, we test these measures on various samples of French bonds. In particular, we find a weak link between the issuer's rating and the level of remuneration demanded by investors. In other words, four rating classes seem sufficient to describe the French market. The impact of rating changes on bond market prices is also studied and the various tests highlight an anticipation of this change by investors.