Assessing Credit with Equity: A CEV Model with Jump to Default
Unlike in structural and reduced-form models, we use equity as a liquid and observable primitive to analytically value corporate bonds and credit default swaps. Restrictive assumptions on the firmâs capital structure are avoided. Default is parsimoniously represented by equity value hitting the zero barrier. Default can be either predictable, according to a CEV process that yields a positive probability of diﬀusive default and enables the leverage eﬀect, or unpredictable, according to a Poisson-process jump that implies non-zero credit spreads for short maturities. Easy cross-asset hedging is enabled. By means of a carefully specified pricing kernel, we also enable analytical credit-risk management under possibly systematic jump-to-default risk.
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