Abstract
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.
Highlights
In this paper we combine a structural credit model with the Heston model of stochastic volatility in a multidimensional framework
We allow the underlying asset processes of the companies to develop with a correlation to incorporate dependence structures among them. This joint model allows for many of the stylized facts known in the literature for equity series like stochastic volatility and leverage effect
With the help of the presented model, the situation of the two mortgage banks Fannie Mae and Freddie Mac was scrutinized. Their default risk was examined at two points in time: mid-2007 and mid 2008. It showed that the already severe situation of Fannie Mae and Freddie Mac before the crisis is compared to the situation in July 2008, when a near end of the two Government Sponsored Enterprise (GSE) was already foreseeable, considering the dramatic increase in the default probabilities
Summary
In this paper we combine a structural credit model with the Heston model of stochastic volatility in a multidimensional framework. 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 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 model parameters These estimators are consistent and quick to be found numerically as shown in this paper which is highly beneficial to practitioners in part due to the negligent literature on consistent estimators for continuous time process with stochastic covariance.
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