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

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Credit scoring is an essential tool used by global financial institutions and credit lenders for financial decision making. In this paper, we introduce a new method based on Gaussian Mixture Model (GMM) to forecast the probability of default for individual loan applicants. Clustering similar customers with each other, our model associates a probability of being healthy to each group. In addition, our GMM-based model probabilistically associates individual samples to clusters, and then estimates the probability of default for each individual based on how it relates to GMM clusters. We provide applications for risk managers and decision makers in banks and non-bank financial institutions to maximize profit and mitigate the expected loss by giving loans to those who have a probability of default below a decision threshold. Our model has a number of advantages. First, it gives a probabilistic view of credit standing for each individual applicant instead of a binary classification and therefore provides more information for financial decision makers. Second, the expected loss on the train set calculated by our GMM-based default probabilities is very close to the actual loss, and third, our approach is computationally efficient.

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