Ebook Explaining the Level of Credit Spreads: Option-Implied Jump Risk Premia in a Firm Value Model
Corporate bonds are defaultable and thus trade at higher yields than default-free government bonds. However, it has been difficult to reconcile this observed difference in yields (the credit spread) with the historically observed default losses of corporate bonds, especially for investment-grade firms (Elton et al. (2001)).
In particular, Huang and Huang (2003, henceforth HH) analyze a wide range of structural firm value models that build on the seminal contingent-claims analysis of Merton (1974). HH show that these models typically explain only 20% to 30% of observed credit spreads for these firms. In response to this credit spread ‘puzzle’ (Amato and Remolona (2003)), a number of authors have recently incorporated jump risk premia into the analysis. As discussed below, the existing evidence on the relevance of jump risk premia is inconclusive.
The contribution of this paper is to use information on the market price of downward jump risk embedded in index put options to estimate a structural jump-diffusion firm value model. We investigate the out-of-sample predictions of the estimated model for credit spreads. As a result, we study whether the price of jump risk embedded in corporate bonds is consistent with the price of jump risk in index options. This is a natural question since index put options constitute the prime liquid market for insurance against systematic jumps, precisely the type of jumps that corporate bond investors are exposed to.
A short index put option tends to pay off particularly badly when the stochastic discount factor is very high and therefore commands a large risk premium. Furthermore, interpreting a corporate bond as a default-free bond plus a short position in a put option on the firm value (Merton (1974)), we effectively test empirically whether the jump risk premium embedded in this firm value put is in line with the jump risk premium embedded in equity index put options.
Our analysis leads to three novel findings. First of all, the results indicate that structural models are useful for the pricing of credit risk, in contrast to the conclusions of previous work. Second, we provide evidence that option implied jump risk premia generate credit spread levels that are quite close to observed spreads and thus relate the credit spread puzzle to the level of average index option returns. Third, we show that incorporating jumps in a firm value model is important to improve the fit of observed option prices and returns, credit spread volatilities and equity volatilities.
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