%0 Journal Article
%T Multidimensional Structural Credit Modeling under Stochastic Volatility
%A Marcos Escobar
%A Tim Friederich
%A Luis Seco
%A Rudi Zagst
%J ISRN Probability and Statistics
%D 2013
%R 10.1155/2013/851419
%X This paper extends the structural credit model with underlying stochastic volatility to a multidimensional framework. The model combines the Black/Cox framework with the Heston model interpreting the equity of a company as a down-and-out barrier call option on the company's assets. This implies a combination of local and stochastic volatility on the equity as well as other stylized features. In this paper, we allow for a correlation between the asset processes of different companies to incorporate dependency structures. An estimator for the correlation parameter is derived and tested in a recovery framework. With the help of this model, we examine the default risk of the two mortgage lenders Fannie Mae and Freddie Mac before their actual placement into federal conservatorship and show that their default risk severely increased during the financial crisis. 1. Introduction In this paper we combine a structural credit model with the Heston model of stochastic volatility in a multidimensional framework. In [1] the value of the equity of a company is modeled as a down-and-out barrier call option on the company¡¯s assets with its liabilities as strike price, following the motivation of structural credit models, for example, by [2] or [3]. As markets have shown, in particular during the financial crisis, volatility is not constant over time. This is why we enhanced the classical structural credit model by providing the asset process with a stochastic volatility such as in the Heston model (see [4]). This simple assumption implies that the volatility of the log-equity is a function of the equity itself (a local volatility feature) as well as the stochastic volatility component of the asset process. The correlation between the volatility of the equity and the equity is also nonzero and negative allowing for the leverage effect reported in the literature. In [1] the default risk of Merrill Lynch was examined utilizing the structural credit model with stochastic volatility. As recent events have shown defaults are unlikely to incur independently. This is why we extend this model to multidimensions by assuming correlation between the asset processes of the companies involved. This dependence structure implies the same level of correlation on the companies¡¯ equity while keeping a rich marginal process for the equities. This paper derives an estimator for the correlation parameter of the assets based on the method of moments which, together with estimators already presented in [1] for the volatility parameters, allows for a full set of closed-form estimators of the
%U http://www.hindawi.com/journals/isrn.probability.statistics/2013/851419/