A mixed integer linear programming model for optimal sovereign debt issuance

Copyright @ 2011, Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in the European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at the link below.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

Applications of optimization to sovereign debt issuance

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel UniversityThis thesis investigates different issues related to the issuance of debt by sovereign bodies such as governments, under uncertainty about the future interest rates. Several dynamic models of interest rates are presented, along with extensive numerical experiments for calibration of models and comparison of performance on real financial market data. The main contribution of the thesis is the construction and demonstration of a stochastic optimisation model for debt issuance under interest rate uncertainty. When the uncertainty is modelled using a model from a certain class of single factor interest rate models, one can construct a scenario tree such that the number of scenarios grows linearly with time steps. An optimization model is constructed using such a one factor scenario tree. For a real government debt issuance remit, a multi-stage stochastic optimization is performed to choose the type and the amount of debt to be issued and the results are compared with the real issuance. The currently used simulation models by the government, which are in public domain, are also reviewed. Apparently, using an optimization model, such as the one proposed in this work, can lead to substantial savings in the servicing costs of the issued deb

Equity Issuance and Divident Policy under Commitment

This paper studies a model of corporate finance in which firms use stock issuance to finance investment. Since the firm recognizes the relationship between future dividends and stock prices, future variables enter in the constraints and optimal policy is in general time inconsistent. We discuss the nature of time inconsistency and show that it arises because managers promise to incorporate value maximization gradually into their objective function. This shows how one could change managers’ incentives in order to enforce the optimal contract under full commitment. We then characterize several cases where time consistency arises and we study different examples where policy is time inconsistent. This allows us to address some outstanding issues in the literature about dividend policy and equity issuance. In particular, our results suggest that growing firms that can credibly commit will pay lower dividends at the beginning and promise higher dividends in the future, consistent with empirical evidence. Our results also suggests that compensation that is tied to stock options creates incentives to inflate prices and pay lower dividends. This is consistent with the empirical evidence of increased stock option compensation and payout through repurchases instead to dividends during the last decades.Stock Issuance; time inconsistency; dividend policy

Quantitative models of sovereign default and the threat of financial exclusion

Business cycles ; Debt ; Default (Finance)

A Stochastic Simulation Framework for the Government of Canada's Debt Strategy

Debt strategy is defined as the manner in which a government finances an excess of government expenditures over revenues and any maturing debt issued in previous periods. The author gives a thorough qualitative description of the complexities of debt strategy analysis and then demonstrates that it is, in fact, a problem in stochastic optimal control. Although this formal definition is conceptually useful, the author recommends the use of simulation to help characterize the set of strategies that a government can use to fund its borrowing requirements. He then describes in detail a stochastic simulation framework, building from previous work in Bolder (2001, 2002); this framework forms one important element in the debt strategy decision-making process employed by the Government of Canada. The primary objective in constructing this stochastic simulation framework is to learn about the nature of the risk and cost trade-offs associated with different financing strategies. To this end, the paper includes a detailed description of the model; a set of possible debt cost and risk measures, including one potentially useful conditional risk measure; illustrative results under normal stochastic conditions; an analysis of the sensitivity of the results to various key model parameters; a novel approach to stress testing; and a possible framework for selecting a financing strategy, given assumptions about government risk preferences.Debt management; Econometric and statistical methods; Economic models

The composition of capital inflows when emerging market firms face financing constraints

The composition of capital inflows to emerging market economies tends to follow a predictable dynamic pattern across the business cycle. In most emerging market economies, total inflows are procyclical, with debt and portfolio equity flowing in first, followed later in the expansion by foreign direct investment (FDI). To understand the timing of these flows, we use a small open economy (SOE) framework to model the composition of capital inflows as the equilibrium outcome of emerging market firms' financing decisions. We show how costly external financing and foreign direct investment search costs generate a state contingent cost of financing, so that the "cheapest" source of financing depends on the phase of the business cycle. In this manner, the financial frictions are able to explain the interaction between the types of flows and deliver a time varying composition of flows, as well as other standard features of emerging market business cycles. If, as this work suggests, flows are an equilibrium outcome of firms' financing decisions then volatility of capital inflows is not necessarily "bad" for an economy. Furthermore, using capital controls to shut down one type of flow and encourage another is certain to have both long- and short-run welfare implications.Capital movements ; Emerging markets

Measuring efficiency of the Farm Credit System

The paper measures the U.S. Farm Credit System’s technical efficiency from 2000 to 2009 using a stochastic frontier production function model with quarterly unbalanced panel data. The paper's results suggest that the FCS has not efficiently utilized their inputs. On an average, the system realizes only 9.7% of their technical abilities in raising their loans, leases and investment. The efficiency of the whole system is estimated to slightly increase over time even during financial crisis period from 2007. Among the system, a significant difference in efficiency between the 5 Banks and the Associations has been found. On average, the Banks have higher technical efficiency of 62.4% compared to that of 7.7% of the associations. The efficiency of the latter increases by a small rate over time during 2004-2009 periods while efficiency of the former is more time-varying and experiences the opposite pattern. No evidence about the impact of financial crisis on the system efficiency was found.Farm Credit System, agricultural lenders, technical efficiency, financial crisis, stochastic frontier production function, financial reform, Agricultural Finance,