Modelling the lifetime of banknotes with a semi-Markov chain model

The quality of banknotes in circulation is important for cash cycles. Central banks continuously try to find new methods for improving the quality of banknotes in circulation, whether by improving the specification of the banknotes or the characteristics of the cash cycle. The way that banknotes deteriorate and the speed with which they do so are some of the main factors affecting the quality of banknotes in circulation and thus, have been drawing the interest of central banks. This study develops a new semi-Markov chain model that could be used by banknote printing companies and central banks to model banknote deterioration. Discrete states of fitness are used in this semi-Markov model to simulate how the banknotes transit between fitness levels. The model requires some input parameters to simulate the cash cycle and present the probability distributions for each state. It is applied to theoretical cash cycles and a sensitivity analysis is performed to identify the parameters that have the greatest impact on the quality of banknotes. This study is the first to apply a semi-Markov model to estimate the lifetime of banknotes. It can be used as a forecasting tool for the proportion of unfit banknotes in circulation.