journal N3 2025

Abstract

The paper discusses the modeling of benchmark bonds for public debt sustainability and, consequently, macroeconomic stability. The importance of benchmarks for financial development is emphasized, while attention is focused on their risks. Modeling these types of financial instruments is important for risk management. One of the methods for this is object-oriented programming and simulations, which are used in modern financial and macroeconomic analysis methods. The paper discusses an example and a small model that is close to reality and simulates the construction of a benchmark. The paper proposes ways to simulate the construction of benchmarks by modeling individual securities using the object-oriented programming paradigm. 

Keywords: Public debt sustainability, Benchmark bonds, Economic modeling, Object-oriented programming

JEL classification codes: C61, H63, E44 

Introduction

In modern times, attention is increasingly focused on public debt. Various economic models have been developed to assess the sustainability of public debt (Berg et al., 2013; IMF, 2013; IMF, 2021). In addition, modern technologies are also considered and the use of blockchain technologies for the sustainability of public debt is also being discussed (Bedianashvili & Gabroshvili, 2024). In the context of modern confrontational globalization (Bedianashvili, 2023) it is interesting to discuss more detailed aspects of public debt.

The paper reviews models for assessing the sustainability risk of public debt. In addition, attention is focused on gross financing needs. Based on gross financing needs and financial development, it is important to model appropriate financial instruments. This mainly concerns benchmark bonds that are important for government debt. Modeling benchmarks, as outlined in this paper, is necessary for long-term liquidity analysis.

The main objective of this paper is to discuss benchmark bond modeling methods for public debt models. The paper uses the object-oriented programming (OOP) method, which is actively used in quantitative finance in the modern period (Schlögl, 2013). This method is used to model the benchmarks in this paper.

Literature Review

The scientific literature on issues of public debt sustainability is extensive, and special attention is mainly paid to its solvency and liquidity when analyzing public debt sustainability. This is well expressed in the International Monetary Fund\'s Sovereign Risk and Debt Sustainability Framework (hereinafter SRDSF) (IMF, 2021). This framework includes various methods that assess public debt sustainability and sovereign risk from different perspectives. Simulations are mainly performed with an annual maturity, and short-term, medium-term, and long-term analyses are used for evaluation. Accordingly, SRDSF offers different tools for each time period. For example, in the short term, a sovereign stress logit model is used. In the medium term, attention is focused on the debt fanchart diagram and gross financing needs, from which a medium-term index is derived. Sustainability is then assessed based on this analysis. Additionally, special stress tests are applied for medium-term analysis, activated under specific conditions. Such stress tests may include banking crises, exchange rate misalignment, commodity prices, natural disasters, and contingent liabilities. For the long term, various modules are used. These modules are for population aging, large amortizations, natural resource discovery/depletion and climate change. In addition, realism tools are integrated to assess the adequacy of the results obtained. For example, analyzing the flows that create public debt is crucial, as it evaluates whether the forecast for debt-creating flows can be justified. The adequacy of bond issuance is also analyzed, where changes in bond maturity are checked. In addition, countries are compared with other comparator group countries and historical data, which refers to 3-year debt reduction and fiscal adjustment. Fiscal adjustment analysis is also conducted separately, using multipliers.

The Debt, Investment, Growth, and Natural Resources (DIGNAR) models (Berg et al., 2013) employ a more dynamic analysis, yielding corresponding impulse response functions. Accordingly, analyzing them allows for drawing various conclusions, including the adequacy of fiscal policy, debt sustainability, its risks, and more.

As the focus shifts to gross financing needs, it is essential to examine benchmark bonds. These bonds play a crucial role in investment strategies and have been extensively studied (Dunne et al., 2007; Remelona & Yetman, 2019). While they can foster the development of securities markets and investments, they also present risks to macroeconomic and financial stability (Arslanalp et al., 2020; Miyajima & Shim, 2014). In addition, benchmark bonds are characterized by reopenings (about reopening see: - U.S. Department of the Treasury, n.d.), during which the volume of benchmark bonds is increased through relevant auctions. Reopenings, and, accordingly, benchmark bonds, can significantly impact gross financing needs over a specific period, thereby creating risk. The aforementioned debt sustainability analysis models do not properly incorporate benchmark analysis, particularly on a quarterly basis, which is crucial for developing countries. Consequently, this paper explores methods for modeling benchmarks using modern techniques.

Modeling Benchmark Bonds

Generally, simulation models can use different methods. Accordingly, since public debt can be given in the form of bonds, it is advisable to model specific bonds. Modeling such bonds involves modeling them in dynamics. For this, it’s possible to take different time periods. It is advisable to model them for a long period, for example, it can be ten years, in order to assess the sustainability of public debt in the long term. In addition to the period, it is also necessary to select a periodicity. Periodicity refers to the time frequency for which the simulation is used for analysis. It is advisable to conduct the analysis at most quarterly, as the effects of benchmark bonds may not be adequately detected in an annual timeframe. For greater accuracy, a monthly timeframe can also be considered, but this may require more detailed information.

Bonds have specific characteristics and accordingly, the payments are determined based on them. Payments generally include coupon and principal payments, although zero-coupon bonds do not pay coupons.

In general, as is known, a benchmark is constructed by conducting various auctions for a specific period. Technically, reopening can be modeled as follows: For example, for simplicity, let\'s assume we want to build a benchmark for the eighth quarter, we conduct an auction and issue securities, with interest paid quarterly. Then at different periods additional amounts are added to previously issued benchmark bond. The reopened security will have the same maturity date and the same coupon rate. For this example, the maturity date would be the eighth quarter. For example, the maturity of a bond issued at the end of the first quarter will be 7 quarters, an additional issue at the end of the second quarter will be fully repaid in 6 quarters, and so on, as shown in Table 1. In this way, all added amounts will have the same maturity date, but it is also important that the coupon rate is the same. To convert quarterly maturity to annual, the maturity expressed in quarters must be divided by 4, since there are 4 quarters in a year. This is shown in Formula 1, where  represents the maturity of the security in years and  represents maturity shown in quarters.

As shown in the table mentioned above, at the end of the eighth quarter, no new additional amount is issued, but the existing one is repaid, which is why the maturity of the new volume will be zero. However, if we want to issue a new benchmark after the payment of the principal of the existing benchmark, which is more realistic, then in the same example, at the end of the eighth quarter we should issue a new benchmark bond with a maturity of 7 quarters, at the end of the 9th quarter we should add additional amount with a maturity of 6 quarters, and etc. In this way, it is possible to construct another benchmark after one benchmark is repaid, and etc. To implement this technically, let\'s assume that the algorithm builds benchmarks not by issuing additional amounts by altering the same bond object (OOP concept), but by creating a new bond object with the same maturity date and coupon rate in each quarter. The general picture of such dynamics is presented in Figure 1, which shows what the annual maturity of each newly issued bond should be at the end of each quarter, if the benchmark bonds are issued for 10 years and another benchmark is constructed after each one matures. Programmatically, this can be done by either mechanically pre-writing the maturities for each future period in an array, or by generating such maturities using loops (e.g., iterators). Compared to reality, this scheme is quite simplified, but it allows the scheme to be easily implemented in simulations, and after its modification, a picture closer to reality can be obtained. For example, in addition to one benchmark, more than one benchmark can be constructed simultaneously, which is closer to reality. In general, in practice, it is common to choose one target quarter and construct a benchmark for that quarter by changing the maturities accordingly in the different quarters so that the additional amounts of the same bond have the same maturity date. Therefore, modeling with the algorithm mentioned above is close to reality. 

Table 1. Maturities for constructing a benchmark for different periods, example

Source: Constructed by the author

Figure 1. Annual maturities required to simulate the construction of a benchmark bond at the end of different quarters

Source: Constructed by the author 

In order to replicate the above-mentioned simplified dynamics in the simulation, then an appropriate program for computer modeling needs to be developed. Since the goal of this paper is to simulate benchmark bonds, then it is necessary to model the reopenings through which the benchmarks are constructed.

Bonds can be modeled using object-oriented programming. Technically, it is possible to use other programming paradigms, but for simplicity, we will use this method in this paper. A bond class must be created for modeling. For simplicity, we will consider par bonds where the coupon payments are made quarterly. The class constructor must specify the coupon value in currency units, the maturity in quarters, and the bond\'s par value in currency units. This class should have the payment method (OOP concept), which will be executed in each quarter of the simulation. If the remaining maturity is zero when checking the maturity, the total payment for the bond will be the sum of the coupon value and the par value, otherwise, only the coupon value will be payable.

For benchmark modeling, a new bond object will be created in each quarter of the simulation from the bond class, which will have a defined par value, coupon value, and maturity according to the scheme and example discussed above, so that if a bond was created at the end of the first quarter, its maturity will be 7 quarters, in the second 6, in the third 5, and so on. This will create a benchmark that is fully paid off in the eighth quarter. This method simulates reopenings. Since we use 40 quarters as the example in the paper, after one benchmark is fully repaid, the second benchmark must be issued in the simulation, if we are to determine the benchmark peaks in the long term. In each quarter of the simulation, each bond in the portfolio must be serviced, and the payments should be recorded in an array for the corresponding quarter. After servicing, a new bond object must be created using the bond class, with the appropriate maturity, coupon, and par value. This bond should be placed in the portfolio array. The array should then be checked as follows: if the remaining maturity of a certain bond is zero, it should be removed from the portfolio. After this, the simulation should advance to the next quarter and continue until the number of projection quarters is exhausted.

When implementing the algorithm mentioned above, in our example, let\'s assume that the bond\'s par value is 20,000 currency units, and the coupon is 500 currency units per quarter. Then, we can see the results of the aforementioned simulation for 40 quarters in Figure 2, where the peaks in debt service that are created in accordance with the above algorithm and displayed in currency units are clearly visible.

Figure 2. Payments of the benchmark bonds in currency units for each quarter

Source: Constructed by the author 

As shown in Figure 2, there were no bond payments at the end of the first quarter because a new bond was issued at the end of that period. By the end of the eighth quarter, servicing costs increase as more reopenings occur. At the end of the eighth quarter, the benchmark bond is fully repaid, and a new bond is issued. In the ninth quarter, since there is only one security in the portfolio whose coupon is being serviced, the servicing cost is low. However, it gradually increases according to the algorithm described above, creating a cyclical pattern.

Conclusions and Recommendations

This paper has reviewed the importance of modeling benchmark bonds for public debt sustainability and highlighted the need for modeling such bonds, which can be of great importance for the economies of developing countries as well. The paper proposes a new method that can be used in benchmark modeling, in particular for analyzing appropriate peaks in the context of public debt sustainability analysis.

The paper discusses how it is possible to construct benchmarks by modeling individual securities using the object-oriented programming paradigm. In general, based on a simple example, two approaches emerged that are close to reality. The first approach involves pre-feeding an array of securities’ maturities into the algorithm, which will then, at the end of each period, create the corresponding object from the bond class that will mature in the specific period. The maturities placed in this array will be placed so that the benchmark built with reopenings (as happens in reality) will be fully repaid in a specific quarter. The second approach involves building a similar array using loops. In addition, after fully repaying one benchmark, another benchmark will be issued.

As for the recommendations, it is advisable to model securities in greater detail so that the modeled benchmarks more accurately reflect reality. In addition, it is necessary to find ways to integrate the developed method for constructing these benchmarks into the framework of public debt sustainability analysis. In this way, the analysis of debt sustainability of specific countries will become more realistic and a more detailed assessment of different types of risks will be possible. 

References:

Arslanalp, P., Drakopoulos, D., Goel, R., & Koepke, R. (2020). Benchmark-Driven Investments in Emerging Market Bond Markets: Taking Stock. IMF. https://www.imf.org/en/Publications/WP/Issues/2020/09/25/Benchmark-Driven-Investments-in-Emerging-Market-Bond-Markets-Taking-Stock-49740

Berg, A., Portillo, R., Yang, S. C. S., & Zanna, L. F. (2013). Public investment in resource-abundant developing countries. IMF Economic Review, 61(1), 92-129.

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Miyajima, K., & Shim, I. (2014). Asset Managers in Emerging Market Economies. BIS Quarterly Review. September.

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Schlögl, E. (2013) Quantitative Finance: An Object-oriented Approach in C++, 1st edition, Chapman & Hall/CRC Financial Mathematics Series. Taylor and Francis, Florida, USA.

U.S. Department of the Treasury. (n.d.). Treasury reopenings. Retrieved June 28, 2025, from U.S. Department of the Treasury website: https://treasurydirect.gov/auctions/reopenings/