CreditGrades Framework within Stochastic Covariance Models

Marcos Escobar, Hamidreza Arian, Luis Seco

Department of Mathematics, Ryerson University, Toronto, Canada.
Department of Mathematics, University of Toronto, Toronto, Canada.
Royal Bank of Canada, Toronto, Canada.

DOI: 10.4236/jmf.2012.24033                

Abstract

In this paper we study a multivariate extension of a structural credit risk model, the CreditGrades model, under the assumption of stochastic volatility and correlation between the assets of the companies. The covariance of the assets follows two popular models which are non-overlapping extensions of the CIR model to dimensions greater than one, the Wishart process and the Principal component process. Under CreditGrades, we find quasi closed-form solutions for equity options, marginal probabilities of defaults, and some other major financial derivatives.

Keywords

Barrier Option; Stochastic Covariance; CreditGrades Mode; Wishart Process; Principal Component Process

Conflicts of Interest

The authors declare no conflicts of interest.

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