An extension of CreditGrades model approach with Lévy processes

This paper proposes an extended CreditGrades model called the Lévy CreditGrades model, which is driven by a Lévy process. In this setting, quasi closed-form formulae for pricing equity options to a reference firm and for calculating its survival probabilities are derived. Moreover, using three tractable Lévy CreditGrades models, we compute implied volatilities on equity options and term structures of credit default swaps (CDSs) and we examine the jump risk effects of the firm's asset value on short term CDS spreads and equity volatility skew. As a result, with this extension, our model is found to have more significant abilities than the original model introduced by Finger et al. [CreditGrades Technical Document, RiskMetrics Group, 2002] and Stamicar and Finger [J. Credit Risk, 2006, 2(1), 1-20], and it is more appropriate for pricing both equity and credit derivatives simultaneously.