Overview
Loss given default specifies the percentage of the value of the asset (Exposure at Default) that is lost when the asset defaults. As and example, when a mortgage defaults, some amount of value can be recovered by selling the house that was collateral for the mortgage.
As a general rule, when an asset defaults, the value recovered may not be known for some time. As in the case of the defaulted mortgage, recovery of value my be process that will take time to complete.
Average LGD
A common way to model LGD is to simply assign it the average loss, that is, to assume that the lgd is constant. This is used in particular in the common portfolio variance approximation.
While making it easy to calculate, LGD can have significant variance which is assumed away in this case.
Beta Distribution Model
The challenge for modeling LGD is that LGD is a range bound variable. In particular, it can only range from 0 to 1. Given these constraints, a common choice for modeling the LGD is to use the beta distribution.
The beta distribution is a distribution that is confined in the range 0 to 1. It is determined by two parameters. Hence, the distribution will be fixed once the mean and variance of the distribution is chosen. THis means that one can measure the average LGD and standard deviation and fit it fairly well with a beta distribution. (see Loffler pg.173)