Introduction to Survival Analysis in Business

Survival model provides not only the probability of a certain event, to occur but also when it will occur ... survival probability can alert a company whether or not a specific account needs a special treatment ... the analysis can be used effectively in retaining existing customers and acquiring new ones in various industries including telecommunication, banking and finance. It has been said that timing is everything - especially in the area of romance. Well, the same may be true in business. Of course, the first thing that might come to mind is the stock market. If we only knew when a particular stock was going to jump in price, we could quit our day jobs! Unfortunately, that kind of information is often not available. What is available is a field of statistics called Survival Analysis. It deals with the timing of events with applications spanning medicine, law enforcement, banking, telecommunications, and a host of other industries. As the field of credit scoring is focused on predicting 'if' an account will become delinquent over a certain span of time, Survival Analysis can tell us 'when.' Survival Analysis is called different things in different industries - event history analysis, reliability analysis, time to failure, and even duration analysis. The purpose of this article is to give an introduction to the subject with an emphasis on how it can be used in banking and finance. However, some discussion will be devoted to Survival Analysis and customer retention - a topic that has seen much attention in the field of telecommunications. SCORING CREDIT Because survival analysis and credit scoring go hand in hand, let's start with a brief discussion of credit scoring. In a broad sense, credit scoring is the application of statistical techniques to determine if credit should be granted to a borrower. It involves collecting information on a set of accounts reflecting satisfactory (good) payment status for a particular period of time (called the observation window) and following their payment performance, say, for a period of one year. At the beginning of the observation window, we may know a great deal about the account - its time on books, how many times it went 30, 60, or 90 days delinquent, its credit limit, etc. We then apply a regression technique that yields a predicted value that will hopefully distinguish between accounts that will either pay or not pay in the year that follows. The choice of the 1-year window is optional depending on the application of the score. What is important to know is that the score does not attempt to describe 'when' the event will occur within the performance window. It only describes the likelihood of the event occurring during that 1-year block of time. To address the timing issue, a more exacting approach is needed - Survival Analysis. SURVIVAL ANALYSIS Let's take a fictitious example in Residential Mortgage for illustrative purposes. Say you conduct a study gathering information on 15 year fixed rate mortgages that are in good standing in January 1995. You then track their monthly performance over a five-year period ending January 2000. In a credit scoring application, you would gather information available in January 1995 on each mortgage, and then determine 'if' there was a default anytime during the five years. However, in building a Survival model, you also record the timing of the default from the point of origin. In this case, because the point of origin is January 1995, we record the number of months until default since January 1995. The reference to the point of origin is essential in interpreting the survival probabilities, which we will discuss shortly. Table 1 shows a part of what you might have come up with. The data in Table 1 needs some explanation. Default is assigned a value of "1" if the loan was observed to have defaulted during the five-year period. However, during the course of the study, you may have loans that were paid-off or sold for a number of reasons. …