Modeling loss given default with stochastic collateral

This article addresses to the appropriate modeling of loss given default (LGD) for the retail business sector. We assume small or mid-size loans that are assigned in a standardized way and collateralized by residential or commercial property. The focus on this specific type of loans entails two major advantages: Firstly, reduction of complexity is followed by easier-to-grasp methodology and increased handiness of results when comparing with other recent approaches in the field. Secondly, the focussing allows to take into account the characteristic properties of the housing market and its underlying uncertainty and so choose a tailor-made modeling for the collateral. The choice of an exponential Ornstein-Uhlenbeck diffusion as the stochastic process of the collateral combines the desirable features with the charm of analytical solvability which seems to be of advantage as regards acceptance among practitioners. Further key improvements of this approach are the explicit consideration of loan ranking, the disentanglement of the time of default and the time of liquidation as well as the introduction of liquidation cost.