Credit Modelling Under Jump Diffusions with Exponentially Distributed Jumps - Stable Calibration, Dynamics and Gap Risk
22 Pages Posted: 15 Sep 2010 Last revised: 8 Oct 2015
Date Written: September 13, 2010
This paper introduces a structural credit default model that is based on a hyper-exponential jump diffusion process for the value of the firm. For credit default swap prices and other quantities of interest, explicit expressions for the corresponding Laplace transforms are derived. As an application of our findings, the model is calibrated to market quotes of fair credit default swap spreads. The time-dynamics of the model are studied, particularly the jumps in credit spreads, the understanding of which is crucial for the valuation of options on credit default swaps such as gap options.
Keywords: credit default, structural model, credit default swap, hyper-exponential jump diffusion, spectrally negative Kou process, entropy-based calibration
JEL Classification: G12, G13, G24, C69
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