The Genesis of Credit-Risk Modelling

The path-breaking work, Merton (1974, Journal of Finance, 29, 449–470), not only addressed a number of important asset-pricing and corporate-finance questions, but was also the genesis of the field of credit-risk modelling. This chapter focuses exclusively on this approach. Not only would it be an injustice to ignore this still-pertinent model, but it offers a range of useful insights into the class of threshold models. The Merton (1974, Journal of Finance, 29, 449–470) framework was conceived and developed in a continuous-time, mathematical-finance setting. To address this complicating factor, a significant amount of effort is allocated to the basic intuition, notation, and mathematical structure leading to a motivating discussion regarding the notion of geometric Brownian motion. Armed with this detail, the chapter proceeds to investigate two possible implementations of Merton (1974, Journal of Finance, 29, 449–470)’s model, which we term the indirect and direct approaches. The indirect approach will turn out to be quite familiar, whereas the direct method requires a significant amount of heavy lifting for its implementation. As in previous chapters, parameter calibration options are explored and both methods are applied to practical portfolio examples.

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