An Integrated Approach to Cost-Risk Analysis in Public Debt Management

2 Introduction . 3 Mathematical Model . 4 Interest rate scenarios . 4 Modelling the dynamics of interest rates . 5 Anchoring the yield curves using exogenous information on short term rates . 9 The debt portfolio cash flow and the balance constraint . 11 The ESA 2010 cost function . 12 Analytical study on the ESA 2010 evolution . 13 The Cost/Risk Analysis . 14 Classical measures of cost and risk . 15 Evolution measures of cost and risk . 16 CVA modelling . 17 Software Architecture . 20 Conclusions . 22 Appendix . 22 Generation of interest rate curves . 22 References . 27 AN INTEGRATED APPROACH TO COST-RISK ANALYSIS IN PUBLIC DEBT MANAGEMENT 2 An Integrated Approach to Cost-Risk Analysis in Public Debt Management Massimo Bernaschi 1,2 Roberto Morea 3 Lucio Sarno 2,4 Fabrizio Tesseri 2 Federica Verani 2 Davide Vergni 1,2 Abstract Public debt management requires accurate analysis of the cost and the risk associated with feasible choices of public debt portfolios. The Italian Treasury employs an in-house, custom-built set of models and software tools aimed at selecting portfolios of securities that satisfy the government’s borrowing needs while fulfilling all the relevant regulatory constraints, thereby delivering suitable tradeoffs between cost and risk on an efficient frontier. In this paper, we present a description of the approach followed by the Italian Treasury, including the study of the dynamics of the cash flow generated by the public debt and the development of stochastic models for the evolution of the main risk factors (i.e., interest rates and inflation). Then, we describe how several dynamic metrics of cost and risks are integrated within a scenario generator in a modular software package called SAPE (Sistema Analisi Portafogli di Emissione – System for the Analysis of Public Debt Issuances). This system supports the public debt manager by providing accurate quantitative estimates of the expected effects of their choices taking into account not only shocks to interest rate curves but also exogenous forecasts about the future behavior of the risk factors. The software can also be used as an accounting tool for the outstanding securities of the Italian public debt, and includes various satellite modules for the evaluation of other relevant metrics, such as the Credit Value Adjustment for derivative instruments.Public debt management requires accurate analysis of the cost and the risk associated with feasible choices of public debt portfolios. The Italian Treasury employs an in-house, custom-built set of models and software tools aimed at selecting portfolios of securities that satisfy the government’s borrowing needs while fulfilling all the relevant regulatory constraints, thereby delivering suitable tradeoffs between cost and risk on an efficient frontier. In this paper, we present a description of the approach followed by the Italian Treasury, including the study of the dynamics of the cash flow generated by the public debt and the development of stochastic models for the evolution of the main risk factors (i.e., interest rates and inflation). Then, we describe how several dynamic metrics of cost and risks are integrated within a scenario generator in a modular software package called SAPE (Sistema Analisi Portafogli di Emissione – System for the Analysis of Public Debt Issuances). This system supports the public debt manager by providing accurate quantitative estimates of the expected effects of their choices taking into account not only shocks to interest rate curves but also exogenous forecasts about the future behavior of the risk factors. The software can also be used as an accounting tool for the outstanding securities of the Italian public debt, and includes various satellite modules for the evaluation of other relevant metrics, such as the Credit Value Adjustment for derivative instruments. The latest version of the paper has been presented during the September 2019 “Public Debt Management Network Conference” organized in Paris by the PDM Public Debt Management Network, an initiative fostered by the OECD, the Italian Treasury and the World Bank to disseminate Public Debt management techniques; it will be published into the proceedings of the conference. 1 Istituto per le Applicazioni del Calcolo “M. Picone" (IAC) CNR 2 Dipartimento del Tesoro Ministero dell’Economia e delle Finanze 3 Sogei 4 Cambridge Judge Business School, University of Cambridge AN INTEGRATED APPROACH TO COST-RISK ANALYSIS IN PUBLIC DEBT MANAGEMENT 3