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1 2001

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Minimisation of public debt servicing costs based on nonlinear mathematical programming approach

Klukowski L., Kuba E.

Control and Cybernetics

2001

Vol. 30, no 1

99-114

The paper presents formulations of optimisation problems for minimisation of servicing cost of government debt instruments (T-bills and T-bonds) issued in Poland and examples of their applications. The first of these problems allows for determining the structure of T-bills with different maturities - from 1 to 52 weeks (sold at multiprice auction), which minimise their servicing cost. This cost (criterion function) is based on T-bills profitability determined by compound rate of return (CRR). The constraints of the task express: * minimum receipts to the State Budget, * maximal profitability, * average maturity, and * minimal and maximal amount for each type of bills. The generalisation of this problem for some series of (consecutive) auctions is also discussed. The second task makes it possible to determine optimal structure of T-bonds using a similar (but more complex) form of the criterion function and more extensive set of constraints. The problems presented are of discrete and non-linear form and in result - rather difficult to solve in real time (during the auction). Therefore, some continuos approximations of these problems based on polynomials determined with the use of least squares method are suggested. Such an approach makes it possible to obtain an optimal solution in several minutes using Excel spreadsheet (package solver) and PC computer. Examples of actual problems for T-bills and T-bonds, based on data for the year 2000 are presented, too. The application of optimisation methods resulted in (relative) gain measured by a criterion function equal to about 1% (annual costs of the domestic debt equals about [3 * 10^9] US$).