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Figure 6. Break-even diagram shows connection between specific LTS, loan term and break-even interest rate.

A number of factors must be considered to decide on appropriate interest rates. It is a complicated process. A formal solution requires acceptance criteria and planning horizons to be known along with significant outside influences impacting business. These include loan quality, macroeconomic situation, customer outflow with prepayment and so on.

Giving reports a visual and an accessible form also matters. RRAS has several visualization options to present optimization solutions in easy-to-read formats. The figure above is one example – it shows a break-even diagram for an actual credit portfolio. Interplay of specific LTS, loan lifetime and break-even rate is made explicit.

It is also worth noting that pricing can be modeled in several different ways, depending on what we must model and calculate:

  • break-even rate
  • optimal rate
  • break-even margin to cover credit losses
  • demand elasticity by loan price
  • loyalty elasticity by loan price

RRAS has advanced functions for optimizing retail loan pricing for any of these and other requests. A user of RRAS can also generate all sorts of business scenarios, macroeconomic forecasts, then use them to receive optimization advice for every scenario and loan lifetime.



The author presents the methods for studying credit portfolio behavior in the Modeling and Stress-Testing Credit Portfolio Behavior are partly based on so-called “dual time dynamics” method. This work suggests using dual time dynamics not for decomposing scalar values but for decomposing matrices. The author considers a credit portfolio as a process described by a first-order heterogeneous Markov chain. Starting from this premise, the author uses vintage analysis and the theorem of strong convergence of modified fixed-point algorithms to arrive at transition matrix decomposition. This method makes highly accurate forecasts of credit portfolios possible. Reserves can be estimated with excellent precision and relevant values for stress-testing obtained.

In his later article The Theory and practice of Retail Credit the author considers some successful practical applications of his methods described in the article “Credit portfolios behavior modelling and stress-test”.