By V. N. Faddeeva

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**Example text**

The approach to building such credit scorecards is essentially one of classiﬁcation. A sample of previous customers is taken and each classiﬁed as a defaulter or a nondefaulter according to their subsequent performance. The idea then is to identify which combination of application and/or performance attributes of consumers best separate the two groups. This idea of such statistical classiﬁcation began with [Fisher (1936)] work on discriminant analysis which can be reinterpreted by saying that it is essentially a regression which tries to estimate p, the probability of non-default, as a linear function of the attributes of the consumer x1 , x2 , .

Suppose for the class of bonds with credit rating j, j = 0, 1, 2, . . , M the price of a bond stripped of its coupon paying 1 at t is vj (t) for t = 1, 2, . . , T then we can calculate the best ﬁt for these values from the bond prices given by solving the following Linear Programme N (ai + bi ) Minimize i=1 T subject to Pi + ai = ci (t)vd(i) (t) + bi t=1 v0 (t) ≥ (1 + m(t))v0 (t + 1) vj (t + 1) − vj+1 (t + 1) ≥ vj (t + 1) − vj+1 (t + 1) ai , b i ≥ 0 for i = 1, . . N ; j = 0, 1, . . , M − 1, and t = 0, 1, .

However in most ﬁrst world countries lending to consumers far exceeds lending to companies and yet that area of ﬁnance is hardly ever mentioned. Yet at the start of the twenty ﬁrst century consumer credit is the driving force behind the economies of most of the leading industrial countries. Without it, the phenomenal growth in home ownership and consumer spending of the last ﬁfty tears would not have occurred. 2 trillion on consumer credit ( personal bank loans, credit cards, overdrafts, motor and retail loans).