Optmization of Treasury securities issuances

Edited by: Institute for applied mathematics "Mauro Picone" - IAC

For a few years the Institute has had a research group in quantitative methods for finance and economics.
Most of the group's research activity is, at this time, concentrated on a collaboration with the Italian Ministry for Economic Affairs for the optimization of the management of the Public Debt in Italy, an issue of paramount importance for the Italian society.

There are a number of possible fixed income securities issued by the Italian Treasury ("zero coupon", called BOT, and bonds with coupons payed twice per year, called BTP, having "maturity", that is expiration date, up to 30 years) and the goal is to find the composition of the portfolio issued every month which minimizes a predefined "cost function".

Mathematically speaking, the problem can be defined as a complex stochastic control problem with strong constraints imposed by national regulations and the Maastricht treaty. The latter, for instance, imposes that:
* the amount of money owed by a government - known as budget deficit, has to be below 3% of the Gross Domestic Product (GDP) - the total output of the economy;
* the total amount of money owed by a government, known as the public debt, has to be less than 60% of the GDP;
The Public Debt is the cumulative total of each year's budget deficit;
* Countries should have an inflation rate not greater than 1.5% of the three EU countries with the lowest rate.
* Long-term interest rates must not exceed 2% of the three lowest interest rates in EU.

The problem is challenging, also because relevant literature is limited, and its complexity is further increased by the need for realistic solutions to take into account several side issues, like macroeconomic factors which are complicated as well.

The stochastic component of the problem is represented by the evolution of interest rates. In order to generate possible "scenarios" of the interest rates' evolution it is necessary to tune the existing models according to the specific case of the Italian market or to develop brand new models.

This is an activity which goes, somehow, in parallel with the development of the optimization model and it is based on the study of stochastic differential equations with properties that are reasonable from the financial viewpoint like the "mean reversion".

At this time the optimizer employs the classic methods of Linear Programming (neglecting possible non-linear effects like the market reaction to changes in the Ministry's policy).

However more sophisticated techniques based on Model Predictive Control strategies (an iterative approach well known in the engineering literature) are under development.
To make it easier for the Ministry's staff to run the optimization tool, a user friendly interface based on a standard browser has been developed.

The current software prototype has been designed to be modular and very effective. Thousands of possible scenarios can be generated and analyzed in a few hours with standard hardware and software components.