We propose a reduced-form model where jumps-to-default are priced because they generate a market-wide jump in credit spreads. While this framework is consistent with a counterparty risk interpretation (e.g., Jarrow and Yu (2001)), it is most naturally interpreted as an updating of beliefs due to an unexpected event. Simple analytic solutions are obtained for the prices of risky debt regardless of the number of firms that share in the contagious response. Empirically, we find that credit events of large firms generate a market wide increase in credit spreads and a significant ‘flight-to-quality’ response in the Treasury market. A calibration exercise suggests that the risk premium for contagion-risk may be considerable, whereas it implies that jump-to-default risk for a typical investment grade firm has an upper bound of only a few basis points.
Recent research has highlighted the fact that structural models of corporate bond prices are incapable of generating reasonable yield spreads (See Eom, Helwege and Huang (2004) and Huang and Huang (2003)). The problem is especially severe among investment-grade bonds with short maturities, where models tend to predict very low credit spreads (Duffie and Lando (2001, henceforth DL). While some suggest the main factors driving bond spreads are taxes and liquidity (e.g., Elton, Gruber, Aggarwal and Mann (2001) and Collin Dufresne, Goldstein and Martin (2001)), others focus on the risk of a jump to default (e.g., Driessen (2005), Berndt, Douglas, Duffie, Ferguson and Schranz (2007)). The latter literature uses the so-called reduced-form models, which directly specifies the jump to default intensity for individual firms. Conveniently, under certain restrictions, these reduced-form models allow to value risky cash-flows by simply discounting under the risk-neutral measure using a default-adjusted short rate. Therefore, defaultable bonds can be valued very similarly to risk-free bonds using standard affine or quadratic models for example.1 Further, by construction, reduced form models can fit any observed risky term structure of credit spreads, even at the short end. However, the implication of large credit spread at short maturities, is that the risk-neutral jump to default probability is high relative to observed historical jump-to default rates. The ratio of risk-neutral (i.e., price implied) default intensity to historical default intensity estimated in these studies is in the range [2,6]. In the reduced-form framework, this ratio can be explained entirely by a risk-premium associated with the actual jump to default itself. Here, we study the magnitude of these implied jump to default risk-premia and their economic implications.
Following the influential work by Bilson (1981) and Fama (1984), an enormous amount of literature on testing whether the forward rate is an unbiased predictor of the future spot rate accumulated over the last years. Excellent surveys are Hodrick (1987), Engel (1996), and Sarno and Taylor (2002).
Although results vary depending on how exchange rates are modeled, the common finding in the overwhelming majority of past research is that the forward rate is not an unbiased predictor of the future spot rate. This forward bias implies the apparent predictability of excess returns over uncovered interest rate parity (UIP).
The recent 2007 – 2009 financial crisis demonstrated, if nothing else, that the financial institutions’ risk management systems were not as adept as previously thought in tracking and anticipating the extreme price movements witnessed during that highly volatile period. Nearly all financial institutions recorded multiple consecutive exceptions, i.e. days in which the trading book losses exceeded the prescribed Value-at-Risk (VaR). In several instances, the total number of exceptions during the previous trading year exceeded the threshold of ten violations which is the set regulatory maximum (Campel and Chen, 2008). Consequently, much doubt was cast and many questions were raised about the reliability and accuracy of the implemented VaR models, systems and procedures.
