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Credit Risk [28]

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Bullet points include: Black-Scholes formulae apply to European-style options, i.e. payoffs only at maturity. So, correspond to assumption that defaults can only occur at maturity of the pure discount debt. Usually (e.g. KMV) models assume American-style options, as more realistic. Defaults can now occur prior to maturity. Default deemed to occur when ratio of assets to liabilities kj,t = Vj,t / Dj,t first crosses a trigger level kj specific to that firm (i.e. j = 1 to m, where m = number of obligors)

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