Incorporating Risk and Ambiguity Aversion into a Hybrid Model of Default
University of Toronto - Department of Statistics
University of Toronto - Department of Mathematics
August 12, 2009
Mathematical Finance, Forthcoming
It is well known that purely structural models of default cannot explain short-term credit spreads, while purely intensity-based models lead to completely unpredictable default events. Here we introduce a hybrid model of default, in which a firm enters a "distressed'' state once its non-tradable credit worthiness index hits a critical level. The distressed firm then defaults upon the next arrival of a Poisson process. To value defaultable bonds and CDSs, we introduce the concept of robust indifference pricing. This paradigm includes both risk aversion and model uncertainty. In robust indifference pricing, the optimization problem is modified to include optimizing over a set of candidate measures, in addition to optimizing over trading strategies, subject to a measure dependent penalty. Using our model and valuation framework, we derive analytical solutions for bond yields and CDS spreads, and find that while ambiguity aversion plays a similar role to risk aversion, it also has distinct effects. In particular, ambiguity aversion allows for significant short-term spreads.
Number of Pages in PDF File: 31
Keywords: Strucutural Models, Intensity Models, Stochastic Optimal Control, Robust Optimization, Indifference Valuation, Defaultable Bonds, Credit Default SwapAccepted Paper Series
Date posted: February 25, 2009 ; Last revised: February 16, 2010
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