In this article, we analyze the impact of risk aversion on the valuation of defaultable bonds, and a simple multi-name credit derivative. Our approach is to work within intensity-based models, as initiated by, among others, Artzner and Delbaen, Madan and Unal, Lando and Jarrow and Turnbull. However, rather than pricing using no arbitrage arguments, we study the utility-indifference valuation mechanism, which entails analysis of portfolio optimization problems under default risk.
A major limitation of many traditional approaches is the inability to capture and explain high premiums observed in credit derivatives markets for unlikely events, for example the spreads quoted for senior tranches of CDOs written on investment grade firms. The approach explored here, and in our related work [28], aims to explain such phenomena as a consequence of tranche holders’ risk aversion, and to quantify this through the mechanism of utility indifference valuation.