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CreditGrades Framework within Stochastic Covariance Models
Department of Mathematics, Ryerson University, Toronto, Canada
Royal Bank of Canada, Toronto, Canada
Department of Mathematics, University of Toronto, Toronto, Canada
- 1 Department of Mathematics, Ryerson University, Toronto, Canada
- 2 Royal Bank of Canada, Toronto, Canada
- 3 Department of Mathematics, University of Toronto, Toronto, Canada
Journal of Mathematical Finance·Volume 02 (2012)·Pages 303–313·Published 19 November 2012·DOI10.4236/jmf.2012.24033
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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.
KeywordsBarrier OptionStochastic CovarianceCreditGrades ModeWishart ProcessPrincipal Component Process
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