Survival Analysis applied in banking field

Survival Analysis is a branch of statistics that takes care of representing development of an event during a period of time.

Its main application is into demography, especially in the analysis of human mortality. Some survival models have been created to produce principally 2 functions: Survival Function S(t), which represents the odds that the event would happen after time t, and Hazard Curve h(t), that describes probability of the phenomenon at time t.

In banking field, one possible application is the description of credit risk. In concrete terms, the event “death” happens when a contract has n outstanding installments (in other terms, having current delinquency equal to n). This analysis is absorbing, because when the contract goes into this bad situation, it will definitively exit from portfolio population. Another way to go out from community is the censor: the contract finishes in advance or it has no outstanding installments during the period of analysis.

Hazard Curve’s notion could resemble another useful banking indicator, vintage absorbing, because the concept is the same: ratio between number of “dead contract” at time t and total number of contracts.

But their trends are completely different due to 2 reasons: vintage numerator is not decreasing (“dead contracts” continue to be considered, differing from Hazard Curve), while denominator is constant (starting portfolio, differing from Hazard Curve where population is decreasing).

Through PROC LIFETEST of SAS, it is possible to make interesting analysis with some aims:

- Compare developments of S(t) and h(t), with a fixed cohort of contracts, according on significant variables; if we consider more variables, SAS calculates every combinations among all the categories.

S(t) e h(t) of car loans of a bank with variable of new/used car

- Compare developments of S(t) and h(t), with a fixed cohort of contracts, depending of levels of current delinquency.

- Compare developments of S(t) and h(t), with a fixed level of current delinquency, depending on cohort (temporal analysis).

SAS program produces automatically graphics and statistics: this study could be useful to understand temporal trends or the way these variables influence credit risk in portfolio.

Furthermore Survival Analysis has a model development, through 2 ways:

- some models evaluating Survival Function S(t) and Hazard Curve h(t), also depending of other significant variables; at the beginning it’s necessary to suppose a specific distribution to estimate parameters (Gamma, LogNormal, LogLogistic);

- some models foreseeing development of Survival Function S(t), depending only by time t; in this process some secondary functions of S(t) are used, because they are mainly alike to a straight line;

In the first case, we’ll have a model as a function of n+1 variables (time t and n significant variables), while in the other, it will depend only by time (through a method similar to linear regression).

Summarizing, Survival Analysis applied in banking field could be useful for some reasons:

- identification of mainly significant variables of a phenomenon
- understanding the influence of these variables on currency delinquency
- development of Survival Function depending on time
- forecasting of Survival Function for next months
- forecasting of Survival Function depending of significant variables