CREDIT-EQUITY MODELING UNDER A LATENT LÉVY FIRM PROCESS

Masaaki Kijima and Chi Chung Siu ()
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Masaaki Kijima: Graduate School of Social Sciences, Tokyo Metropolitan University, Tokyo, Japan
Chi Chung Siu: Finance Discipline Group, Business School, University of Technology, Sydney, NSW, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 03, 1-41

Abstract: Recent empirical studies have demonstrated the informative nature of the equity returns in explaining the variation of the underlying firm's credit default swap (CDS) spreads. Motivated by these findings, we propose a unified credit-equity model by extending the latent structural model in Kijima et al. (2009). As in the original latent model, we treat the actual status of the firm to be unobservable and one can extract information from the marker process that is observable to the investors. Default occurs when the actual firm value drops below a default threshold for the first time. Different from the model in Kijima et al. (2009), however, we define the marker process to be the firm's equity process. Choosing firm's equity process to be a marker process subsequently relaxes the restrictions imposed in Kijima et al. (2009), enabling us to price firm-related securities.Additionally, we enrich the original latent structural model with jump and regime-switching dynamics. The purpose of the extensions is to capture more realistic credit spreads and implied volatility skews under different economic environments. The proposed model maintains analytical tractability even under such complex dynamics, for the prices of CDSs and equity options admit semi-closed-form solutions. In sum, our model can evaluate corporate securities and their derivatives in a unified framework.

Keywords: Regime switching; jump-diffusion process; credit-equity modeling; credit derivatives; equity derivatives; first passage probabilities; Laplace transforms; numerical Laplace inversion (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0219024914500216

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