In this paper we present a valuation model that combines features of both the structural and reduced-form approaches for modelling default risk. We maintain the cause and effect or 'structural' definition of default and assume that default is triggered when a state variable reaches a default boundary. However, in our model, the state variable is not interpreted as the assets of the firm, but as a latent variable signalling the credit quality of the firm. Default in our model can also occur according to a doubly stochastic hazard rate. The hazard rate is a linear function of the state variable and the interest rate. We use the Cox et al. (A theory of the term structure of interest rates. Econometrica, 1985, 53(2), 385-407) term structure model to preclude the possibility of negative probabilities of default. We also horse race the proposed valuation model against structural and reduced-form default risky bond pricing models and find that term structures of credit spreads generated using the middle-way approach are more in line with empirical observations.Stochastic term structure, Defaultable bond, Credit spread, Probability of default, Hazard rate,
In this study, we use a factor model in order to decompose CDS spreads into default, liquidity, systematic liquidity and correlation components. By calibrating the model to sovereign CDSs and bonds we are able to present better decomposition and more accurate measure of spread components. Our analysis reveals that sovereign CDS spreads are highly impacted by liquidity risk (i.e 50% of default risk and 49.91% of liquidity risk) and that sovereign bond spreads are less subject to liquidity frictions and therefore represent a better poxy for sovereign default risk (i.e 97.08% of default risk and 1.73% of liquidity risk). Furthermore, our model extension enables us to directly study the effect of systematic liquidity and flight-to-liquidity risks on bond and CDS spreads through the factor sensitivity matrix. Although these risks do have an influence on the default intensity, the magnitude of their impact is small and therefore they do not contribute significantly to spread movements.
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