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Title: A piecewise linear approximation approach for the simultaneous optimisation of price and loan-to-value Authors:  Marius Smuts - North West University (South Africa) [presenting]
Fanie Terblanche - North West University (South Africa)
Abstract: In a competitive financial industry, one of the challenges for secured retail lending products is to determine the optimal prices (i.e. interest rates) that maximise both the loan take-up probability and expected revenue. However, the technologically driven and competitive nature of the financial industry require the computation of the optimal prices for secured lending products be performed as efficiently, accurately and timeously as possible, while still adhering to certain risk distribution constraints. We discuss a response model which relates take-up probabilities with price and loan-to-value (loan amount expressed as a percentage of the value of the underlying asset), hence taking into account a customer's willingness to pay for a loan. A piecewise linear approximation approach is then followed to simultaneously determine the optimal price and loan-to-value percentage for a potential customer. Furthermore, in an attempt to reduce computing times, linear interpolation is applied to these optimally calculated values.