A mixed integer linear programming model for optimal sovereign debt issuance

Governments borrow funds to finance the excess of cash payments or interest payments over receipts, usually by issuing fixed income debt and index‐linked debt. The goal of this work is to propose a stochastic optimization‐based approach to determine the composition of the portfolio issued over a series of government auctions for the fixed income debt, to minimize the cost of servicing debt while controlling risk and maintaining market liquidity. We show that this debt issuance problem can be modeled as a mixed integer linear programming problem with a receding horizon. The stochastic model for the interest rates is calibrated using a Kalman filter and the future interest rates are represented using a recombining trinomial lattice for the purpose of scenario‐based optimization. The use of a latent factor interest rate model and a recombining lattice provides us with a realistic, yet very tractable scenario generator and allows us to do a multi‐stage stochastic optimization involving integer variables on an ordinary desktop in a matter of seconds. This, in turn, facilitates frequent re‐calibration of the interest rate model and re‐optimization of the issuance throughout the budgetary year allows us to respond to the changes in the interest rate environment. We successfully demonstrate the utility of our approach by out‐of‐sample back‐testing on the UK debt issuance data.